## Testimonials: The Community in Support of BIRS

This was an extremely helpful workshop. There are several groups that use higher (i.e. parametrized) Morse theory techniques, but they don't talk to each other. This conference was the first real progress towards establishing relationships between the fields. It was a major success.

Every time I visit BIRS, I come back with a new project, new collaborator, or new development in an old project - something that can't be said about many conferences.

It was a wonderful experience to be at BIRS. The following developments would not have happened (at all or as quickly) without the visit to Banff: 1) I gave a talk on "p-permutation equivalences", a relatively new concept in the theory of blocks of finite group algebras. After the talk, Jürgen Müller and Susanne Danz approached me with the suggestion to write a computer program that would allow to compute and analyze p-permutation equivalences and more generally p-permutation modules. We met for about 3 hours, discussed possible algorithms, and have now an initial concept. Motivated by this quick progress we agreed to meet for a week in July to continue with the project. Computations of specific examples would be very enlightening, especially in order to settle or provide more evidence on uniqueness questions. 2) There is a logical hierarchy between different types of equivalences of blocks of finite groups. Discussions with Jeremy Rickard and Markus Linckelmann gave me new ideas how to construct p-permutation equivalences that do not come from the stronger notion of a splendid Rickard equivalence. Examples of this type are currently unknown. 3) In collaboration with Susanne Danz we continued to complete a paper that we started more than a year ago on the quasi-heredity of certain category algebras. "Skype" or similar media would have been far less efficient for this purpose.

This meeting was a marvelous success and I enjoyed every minute of it. I guess much has been said about the comfort of the venue and the beauty of the surroundings. It might be added that the new auditorium is very intelligently conceived and that the recorded talks were very appreciated. For me the event was a unique opportunity to discuss the maths I am presently working on, having focused on this theme in the last three years. I particularly enjoyed the very interesting and carefully prepared session about the remaining problems in checking for simple groups of Lie type the inductive conditions available for certain global/local conjectures. In all it was a very fruitful meeting due to the presence of almost all experts of the field, plus a couple of other experts in neighboring subjects, like Ben Elias whose talk and enthusiasm I appreciated very much. It is also very positive that this meeting could invite many junior researchers (post doc and PhD students). I had a series of informal discussions with many participants. With Tiep I discussed the possibility of proving certain stabilizer statements in the case of finite symplectic groups from the existing literature he knows well. With Brunat, following Gramain's talk on their joint work, I discussed the possible applications of the representation theory of wreath products and the related Morita equivalences to the proof of more equivalences between blocks of Weyl groups or Hecke algebras of classical types. I had many discussions with Paul Fong about the relevance of the joint work with Broue and Srinivasan on Dade's conjecture in the case of unipotent blocks of finite reductive groups, especially in view of recent results by Spaeth producing a reduction theorem for that conjecture.

I found the workshop at BIRS very inspiring. Besides many interesting talks on recent results and trends in global-local representation theory of finite groups, the meeting also provided ample opportunities for personal discussions with colleagues from all over the world. Here are some concrete research activities resulting from the workshop at BIRS: Inspired by Robert Boltje's (UC Santa Cruz, USA) talk on Tuesday, he, Jürgen Müller (University of Jena, Germany) and I started to discuss possible strategies for investigating $p$-permutation equivalences between blocks of finite groups computationally. During the problem session on Thursday afternoon we developed some concrete ideas, and we now plan to meet again this summer to pursue our joint project. Moreover, during the free afternoon on Wednesday, Robert Boltje and I had the chance to make significant progress on another joint project (on quasi-hereditary twisted category algebras), which we had started several months ago, but were not able to complete just via email or Skype correspondence.

I found the workshop at BIRS very stimulating. Meeting all the renowned experts in the field was a very interesting and motivating experience. My research background is only tangential to the topic of the workshop, but I am eager to learn more about this topic and I will continue my research in this direction. (More precisely, I am working on classifications of objects which are vital for the local/global conjectures discussed in the workshop.) I also bought two books, written by participants of the workshop, and I will do more research in this field. The stay was wonderful! Thank you very much! I am looking forward to coming back in November!

School of Mathematical Sciences, Monash University

I enormously enjoyed my stay at BIRS; the workshop was very inspiring for me. Besides getting a great overview on current developments and meeting and discussing with people whom I haven't seen for a while, I found particularly useful the problem session/discussion, in which a variety of problems (from major directions to important obstacles of a mere technical nature) were explained and possible ways discussed on how to overcome them. This certainly provided some fresh insights for me which -- I hope -- may even lead to some new research projects and collaborations.

The conference was a great success; it was excellently prepared and managed by the organizers and the people at BIRS. Most of the talks reported on recent progress on conjectures by Alperin, Brauer, Broué and McKay. It was exciting to see that we are really coming closer to the solution of some of these longstanding open problems. There was also sufficient time for exchange and cooperation with the other participants. I personally profited, in particular, from discussions with M. Geline, M. Linckelmann and A. Turull on vertices of simple modules and characters. R. Kessar, M. Linckelmann and I are in the course of preparation of a manuscript on this topic which will hopefully be available in a few weeks or perhaps months. We are all very grateful to the BIRS for providing such excellent facilities for mathematics and hope to return some time in the future.

[As a result of the workshop], I have started a new line of research with M. Linckelmann about characterizing nilpotent blocks, which is a possible continuation of one of my recent papers. Also, with my coorganizer P. H. Tiep, we have started a possible refinement of McKay in groups with nilpotent Hall subgroups. About my student C. Vallejo, she gave her first important international talk, and she already has an invitation to visit Kaiserlautern with Gunter Malle for some months to join his team working on the McKay conjecture. The talks were, in general, excellent. The discussion session on the route plan to prove the global/local conjectures was very useful for researchers, to know where we are exactly, and for younger researchers (and even senior ones) to join us in the plan of proving them.

Algebra, University of Valencia

I want to thank the organizers once again for a very nice workshop and the opportunity to speak. It was very beneficial to be able to meet (or see again) many people in the field, both those who are well-known in the area and also fellow early-career mathematicians. Following my talk, there were some very good recommendations and discussions, for example with G. Malle, G. Navarro, and J. Taylor, which may help my progress on one of my current problems. I also had the opportunity to speak with G. Malle and P.H. Tiep about future directions for my research involving the inductive Alperin-McKay and BAWC conditions, as well as S. Koshitani about new ways to simplify some arguments in my earlier work on the inductive conditions, which will be quite helpful in my future research.

The workshop on Global-Local Conjectures in Representation Theory of Finite Groups was very successful. The participants were a good mix of senior and junior mathematicians, and there were lectures by both. I had discussions with several participants. One lecture in particular by Olivier Dudas on work he was doing with Gunter Malle (an organizer) gave me insight into my research and leads I can pursue. Among new contacts I would specially mention Ben Elias, a young mathematician who is doing cutting edge research. On the final day Gunter Malle gave an overview of where the program on Global-Local Conjectures stands, which would be very useful for both people working in that area now and for those interested in starting to work in it.

I would like to thank BIRS for giving us this opportunity to hold the workshop at the excellent venue and in the highly stimulating environment of the Banff International Research Station! During my stay at BIRS, aside from organizational tasks and attending interesting lectures and brainstorming discussion session, I was able to start a new research project with my collaborator Gabriel Navarro, as well as continue our collaboration on ongoing projects that aim to resolve some basic questions on representations of finite groups. Together with Gunter Malle and Frank Luebeck (and in discussion with Jean-Baptiste Gramain and Olivier Brunat), I had started another new research project with the aim to answer a question of R. M. Guralnick concerning representations of finite quasisimple groups. I also had discussions with other participants, including Marc Cabanes, Gerhard Hiss, Klaus Lux, Bhama Srivasan, and Amanda Schaeffer Fry.

Although this was not the first time I was invited to BIRS, it was the first time I was able to come. I was very impressed by the organization, and how well the facilities were administrated. The scientific aspects of the conferences were likewise excellent. The topics of the conference had a clear focus on the proof of a number of global/local conjectures in the representation theory of finite groups. The participants are making important and related progress on these, and exchanging ideas and divvying the work to do next is essential. I was particularly interested in learning the current status of these conjectures, including some new ones. I am pleased that there is substantial progress on many of the simple versions of the conjectures. At the same time, there is still a lot of work to do on the more refined versions of them. While there, I enjoyed productive mathematical discussion on these and related topics with a number of researchers, including Michael Geline, David Gluck, and Burkhard Kuelshammer. These and other informal exchanges affected a number of papers on these conjectures that I am in the process of writing, and suggested new promising avenues of research. It was an excellent and productive experience all around.

I wish to thank you and the organizers for this very interesting workshop. The main interest comes from the pleasure to receive the latest news about their current research from the top researchers directly. On a more personal level, my research made some progress in two directions. On one hand, one of the organizers informed me about the existence of a counterexample (in high dimension) to a conjecture on which we had started to work (proof of the dimension 1). On the other hand, with another participant, we initiated a new line of research. He presented me a new conjecture, which extend a result of mine, and we started to think about it. We already established an interesting particular case of it.

The workshop was very productive, as always in Banff. I learned a lot of useful things and problems... Excellent job!

I got many new ideas for future research and discussed connections between my work and other fields and problems.

The workshop on Geometric Tomography and Harmonic Analysis was a really impressive event that is directly relevant to my current research in convex and stochastic geometry. Most of the talks I found really inspiring, some of the talks will have direct impact on my recent research directions. The style of the workshop - its size, informality and schedule - was perfect, the atmosphere at the Banff Center was ideal.

The workshop was excellent. It left me with several questions and possible problems that I can see can be investigated. Also, a possible new collaboration did come about.

Great facilities, excellent research environment, which gave me the opportunity to start and/or continue several collaborations. Thanks a lot.

Great workshop. I've learnt so much that I left as a different person. Thank you so much.

I truly enjoyed the last week tremendously! I put my impressions on my blog: http://xianblog.wordpress.com/2014/03/07/advances-in-scalable-bayesian-computation-day-4/

One of the best and most useful workshops I have attented so far!

I was one of very few PhD students to attend this BIRS workshop, and I was a little apprehensive that I would not know enough to be able to meaningfully contribute. I found that I was more than adequately prepared for a number of talks (those most related to my research) and less than adequately prepared for some others. This helped solidify in my mind what were the "hot-topic" areas of my field, and introduced me to many avenues for future research. The collaborative spirit that pervaded the workshop allowed me to have meaningful conversations with world-renowned researchers in my field. A few months ago I was struggling through a particular paper in connection with my research. At the BIRS workshop, I sat at lunch with the lead author and asked him my questions in person! To get to meet and discuss these exciting ideas with the best and brightest was a real privilege that I will long remember. I think that the relationships I forged in Banff may yield fruitful collaborations and/or post-doc/employment opportunities in the future.

My participation will greatly impact my future research projects since this WS@BIRS gave me the opportunity to meet new potential collaborations and to elaborate new directions with my existing ones. We have already planned next meetings and cross-fertilization between theoretical aspects and applications. This nice endeavor is coming up! Great place, great workshop, fantastic atmosphere, strong opportunities for future collaborations with new people. The logistic is optimal, the local organization committee is excellent. The atmosphere is "My pleasure is to assist you."

NeuroSpin, CEA

The BIRS workshop has an impact on my current research in order to have a fresh insight on some of my research projects.

School of Mathematics, Cardiff University UK

I have had contacts I would not have had otherwise, with people working on multifractal analysis. With my collaborators and students we are currently working on image retrieval as well as recognition of melanoma lesions. In both subjects we mean to apply multifractal analysis. The workshop has certainly had an influence on this decision. Thank you!

Computing Department, FCEyN, University of Buenos Aires

I want to thank you for this great week at BIRS. It was a huge opportunity for me to make new contacts and research projects than I wouldn't have had otherwise. Also, now I'm aware of other workshops organized by people I met last week. Thanks again for your enormous work!

The workshop was really great. The place is a wonderful place to work, with all the equipment (wifi, computers, meeting rooms...) It is a bit soon to know how it will impact my research, but at least one new collaboration might arise from the workshop, and maybe an other one. I also have new contacts I probably would not have had otherwise.

This was a great conference. The organizers have done a fabulous job. I find the talks to be a good mixture of theory and Applications. The participants have diverse background, rating from math to physics to engineering. This is very helpful for many of us to learn things form one another. The food and scenery can't be beat, too ;)

One of the main benefit of this workshop is to mix people from different communities, working on a common subject. It allows to have a good overview of the state of the art on the subject while sharing some ideas, some problems, some solutions... I think the workshop will open new directions in my research, from the most fundamental aspect to the validations of the methods I have proposed to model the contact. I also think that it was a good opportunity to share our experience on different simulation platforms. We had the opportunity to show the results obtained with our open-source framework SOFA and discuss them with people that are involved with other platforms (siconos, chronos, ...), with different application focus. I think the idea of providing benchmarks for assessing the quality of these platforms is very important. It was PERFECT! (special thanks to the chef... the food was excellent!) Do not change anything!

Shacra Team, INRIA Lille

This workshop is of utmost importance to support a small extremely cross disciplinary community such as ours. It allows us to exchange research experience and knowledge across diverse fields such as computer science, mathematics, physics and engineering. On a personal level I extracted important knowledge about how our research field is maturing and developing. An important observation is that many independent research groups are seeking a methodology for validation. Hence without this workshop such efforts may not have been unified. With this workshop everybody has joined efforts in collecting data for creating benchmarks -- an important step for our field.

Thanks for letting us have this great workshop! It had never learned so much about contact mechanics in such a short amount of time. More importantly, mixing people from different academic communities (math, robotics, graphics) provided a unique opportunity to meet so many interesting people and discuss ideas and possible collaborations. This allowed me to start discussions about at least two exciting new collaborations. I sincerely hope that this will take place again.

I found it extremely informative and interesting and it gave me a number of new things to think about, and kick started a few new projects. Specifically: 1. Interaction with Jeff Trinkle and Ying Lu on using the PATH solver for nonlinear versions of the friction contact problem arising from real data. Ideas sparked about how to use MPEC in conjunction with these models. Clearly this was influenced by the talks given by Ferris and Lu at the meeting. 2. Interaction with Vincent Acary on an iterative solution technique for the friction cone problem. Motivated by talks by Acary, Pang and Anitescu. 3. Further interaction with Negrut and his students (at Wisconsin)! Ideas on how to collaborate to use conic solvers (interior point versions) on their data sets. 4. New thoughts related to the use of logic programming and complementarity. Thinking about ideas on how to formalize this, and when it would work well. Lots of other things might come from the meeting, but these are clearly things that are foremost on my mind after the talks and discussions at Banff.

The workshop was extremely helpful in understanding what are the state-of-art in computational contact mechanics, providing a forum for researchers from different background (Math, OR, ME, CS, Geo-Science, etc.) working on the similar problems to discuss and exchange ideas, and shared recent work. Wow! What a collection of brilliant minds with different perspectives working on similar problems in one place! CONGRATS to the organizers' excellent planning and organization! I've certainly met several new researchers from other disciplines, as well as those within my own community. I'm also looking for postdoc, though I did not find any suitable candidates at the workshop, I did spread the words. The new contacts I made should be very valuable in my future endeavors in expanding my current research projects into other related topics and ideas that I've in mind. I've found new energy and new directions in a relatively short time there. The workshop was absolutely fabulous and planted new seeds for future projects! THANKS! The local arrangement, rooms, and meals were excellent! This is a wonderful facility and I very much appreciate the opportunity to be able to take advantage of the workshop and the facility.

Computer Science, University of North Carolina

The BIRS workshop on computational contact mechanics was one of the best workshops that I've attended. I was able to network with the top researchers in this field and discover the state-of-the-art in terms of modeling contact. For example, studying the formation of rivers by modeling particles flowing in a fluid and speeding up the solution of the algorithms using advanced optimization techniques. BIRS created a relaxing and conducive atmosphere for learning and collaborating. I learned from, presented to, and conversed with THE top researchers in my field. Needless to say, I walked away from BIRS with an incredible list of contacts. The workshop provided an impetus for a larger collaboration effort across the field. This effort will eventually help standardize the methods of testing and validation for the entire discipline. The BIRS facility was amazing and the staff were absolutely wonderful.

Mechanical Engineering, University of Wisconsin - Madison

The BIRS workshop on Contact Mechanics brought together researchers from a variety of fields including mathematics, robotics, computer graphics, and geology to discuss the state of the art in contact simulation and analysis, as well as to discuss open problems. In my robotics research, many of the most challenging problems are deeply tied to the difficulty of analyzing contact mechanics. This workshop brought me together with some of the best researchers in contact modeling, whose approaches have deep connections to my formal analysis of robotic stability. Not only did I make some invaluable contacts for future research, and my future job prospects as a current graduate student, but some of the discussions at the workshop have produced immediate results in my algorithm development. While the workshop finished just weeks ago, and I have not yet written any new papers, I have no doubt that some of these ideas will lead to future publications and research.

This is my fifth Banff meeting (Muscles x 2 + non-holonomic mechanics + balance + contact =5). I am always happy to come back because: I like small meetings. The setting is lovely and inspiring. The accommodations are great (well, too great), e.g., Good vegan food, Nice rooms, Basketball, etc. The meeting logistics are well done: Good meeting rooms. Good support staff. Good lounge room for evening discussions. Good internet. About this meeting in particular. It introduced me to many people with whom I have overlapping interests but whose work I did not know. In particular, through the talks and evening discussions I have finally got a sense of the issues of concern to those who do large scale simulations with contact. I also learned about the capabilities of the packages and as a result of this meeting I am more or less committed to collaborations with two of the groups at this meeting. Because of the time for discussions at this meeting, both groups were able to describe their computation abilities well enough so I could get a sense if they would likely be of use for my lab. On the flip side, the meeting gave me an opportunity to share some of the more physical things that I think about with a community that can make use of those insights.

Mechanical engineering., Cornell University

The workshop has been fantastic. Having a focused theme, but with people from a variety of backgrounds (engineering, robotics, computer science, mathematics) has been especially valuable. I, myself, have taken away two ideas that have the potential to become publications. They will need continued development away from the workshop, but they would not have started without it. One of these involves a new collaboration for me. I already knew some of the participants, but many (actually most) were new to me or I knew only by reputation or papers. Some participants "prodded" intellectually, and have forced me to re-think some things I had taken for granted, or had not taken as seriously beforehand. I am going to be doing some calculations to see if my assumptions are as well-founded as I thought. Thanks for the workshop. It has been very invigorating.

Mathematics, University of Iowa

I thoroughly enjoyed the workshop last week. It was one of the best meetings I have been to in recent memory, due to both the technical strength of the participants/material and the fantastic venue. It absolutely broadened my perspective by introducing aspects of the field that I had not been exposed to previously. Thank you for your support!

The workshop was amazingly successful. We got a number of email thank you notes like the one below: "Organizers,This is the best meeting I have ever attended. As a graduate student, I attended international conferences in which communication was largely stratified (professors mostly spoke with professors, and students with students). Due to the intimate size of the meeting, the shared meals and housing at BIRS, and the egalitarian attitudes of the participants; I felt much greater connection to the other participants. I would emphasize the importance of the meals and informal social gatherings, at which technical discussion continued. During this meeting, I was exposed to a number of open source physics solvers that I would like to investigate for connections with our open source robotics software packages (I compiled Chrono Engine, Sofa, and Siconos on my laptop this past week). I'm also looking forward to developing a set of benchmark contact problems in order to compare the different methods that we use."

Computer Science, Rensselaer Polytechnic Institute

The workshop was fantastic. I was introduced to the people behind the work I know so well, as well as what they're currently working on. The talks and interactions I had during the week certainly have helped me in better understanding the ideas and concepts of my field, and I feel as though my own work benefited greatly from the insight and input of the other attendees. As a result of the workshop, I believe that we will as a group pursue a database of benchmark problems for multibody dynamics that will prove invaluable to the progress of our field.

The participation in the BIRS workshop on "big data" benefited my research in several ways. First of all, I was able to present my own work to a group of researchers working in different areas in statistics and learn from their comments and suggestions made from different angles. These expertise broadened my sight and gave me more insight into my research problem. Some of the things that I learned in this workshop, though not directly, are helping with my current project. Second, the topic of this workshop, "big data", was something that I was not very familiar with before attending this workshop. Through this workshop, by involving in the talks and discussions, I learned about the problems, current development, and future unsolved challenges in this field. I now think this area is very important while requiring more attention and research. Third, this one-week workshop created a very friendly environment that people can closely interact and focus on research without much disruption. I personally got to many of the experts in this field and learn from both their talks and informal discussions. Some of these people I would not have met if it were not in a small and concentrated workshop like this one. I am really grateful for the workshop organizers and local staff at BIRS who made all these possible to me.

Biostatistics, Yale University

This is one of greatest workshops I attended so far. It gave fresh information on the research status of Big Data Analysis and activated some new research projects (or collaborations) related to Big Data Analysis. In particular, I have got contacts with some front players in this new emerging field and have learnt several new software about Big Data Analysis. I start rethinking my current research projects by exploring the utility of Big Data Analysis. I am working on statistical genetics and neuroimaging. I have seen from this workshop that the two fields start integrating each other. Some exciting discovers will appear next few years.

School of Mathematics, Statistics and Actuarial Science, University of Kent

I believe that the talks in the conference are high quality. I have found that I can continue to do something along the same directions. Nice organization. BIRS is super.

Biostatistics and BRIC, Univerity of North Carolina at Chapel Hill

My participation had remarkable impact on my research and I had stimulating discussions about problems I currently working on or thinking about with some of the experts in the field or related fields. There are also prospect of some collaboration on future papers with some of the workshop participants.

Mathematics, University of Pittsburgh

I participated in a so-called half workshop, but the partner conference was very close to our own subject. In particular, the participants of both workshop new each other well. This made it possible to create some interaction between both workshops, including joint talks. I liked this idea a lot. It gave us the opportunity to look at related subjects, too. The atmosphere at Banff was really nice and stimulating. I was glad that I was able to visit this place again.

I very much appreciated my participation in the BIRS workshop. It has been a great opportunity to meet experts in a field which is very close to my current research interests, especially mathematicians from the US, Canada or Russia, which seldom visit my home country. The talks by Kiumars Kaveh, Valentina Kiritchenko, Nicolas Perrin, and Evgeny Smirnov were especially interesting for me, as well as subsequent discussions on their recent results. I also had stimulating discussions with Jochen Kuttler about my latest work, and I established new contacts with several junior mathematicians including Izzet Coskun, Chris Manon, Henrik Seppänen. The workshop had a very significant impact in the development of the theory of Newton-Okounkov bodies, a currently very active topic with experts scattered in many countries. It also had (at a smaller scale) consequences on my own research, by showing which lines of investigation would be of interest in this theory.

Institut Fourier, Université de Grenoble

It was a very intense and POSITIVE week. The conference was very interesting, the participants were all very motivated, the conference room and all facilities were very comfortable and and everything needed was there. The location was incredible, I hiked a little bit whenever I had time, I just regret I did not have more time to relax in this incredible place. My deepest thanks to the organizers and to BIRS and Banff Centre staff.

Some of the talks were very inspiring, and they will certainly have an impact on my current and future research. During the conference I started some new research projects with people at the conference. I wouldn't have started these joint research projects otherwise. The scientific organization and the BIRS accommodation and organization were truly great. The BIRS hospitality and organization were simply perfect.

Mathematics, Universita di Roma, Tor Vergata

My participation in the BIRS workshop did impact my current research on toric vector bundles. Specifically, time spend with my collaborators at BIRS lead to new discoveries and results. Feedback from our presentations also lead to new insights. Although it is too soon to be sure, some conversations from the workshop may develop into new research projects and new collaborations.

The workshop was a great moment to discuss research with people in my field. Me and my coauthors have had good feedback and ideas. It was also a good occasion to meet people that I would have hardly met in person and discuss math in an intensive way. In particular the location is great and it stimulates a lot the scientific activity.

First I have to congratulate all the BIRS, from the very concept of having an excellent place to work, to share experiences and knowledge, to the logistic facilities that allow people with same objectives to gather in a productive way. The staff to support the work is also perfect. It looked to me almost unreal that we can actually have such a place. For me the workshop was truly profitable in a wonderful atmosphere. I have met people from different places yet with same ideals and I could share the professional experiences of Mathematicians contributing to Mathematics Education. The number of people with specific profile attending the workshop was also a key ingredient to the success, but of course the effort of the organizers (Sol Friedberg, Ed Barbeau, Bill McCallum, Patricio Felmer and Jose Antonio de La Peña) was determinat. I express here my gratitude and appreciation to BIRS for this wonderful experience.

I must say that it has been a wonderful experience I won't forget. I want to thank the generosity of all participants. They shared their ideas, their initiatives, their experiences and at the same time they were eager to know about what is happening in other places of America. Attending the workshop showed me that it is of the highest importance involving in mathematics education issues. This meeting let me learn many things, gave me ideas and also, let me think about cooperation with mathematicians from America interested in mathematics education. Finally, I want to thank BIRS for providing such a marvelous enviroment.

I found this conference very stimulating and informative, learning the latest about the state of math education in the Americas and the efforts of mathematicians to improve this education. Our conversations also included serious discussion of ways to share resources and help each other in working in this area. I am optimistic that the workshop will have a long-term effect upon international cooperation among mathematicians in the Americas concerned with math education.

Department of Mathematics, Boston College

It was a fascinating and inspiring workshop. Of course, since the topic was math education, it did not help my research program in any direct way. However, as a professor at a university where half of our math undergraduates want to be high school teachers and one of our graduate M.A. programs is specifically for in-service teachers, it was certainly highly relevant to my professional life. It was my first exposure to math education in Latin America, and in some ways they are better organized than we are. It was also noteworthy that the majority of the people there were active innovators in teacher education (I don't count myself as one of them) and simultaneously active mathematics researchers. Thanks as always to BIRS for the great organization and facilities and financial support (especially since we can't use NSERC funds for this meeting).

The Pan-American Workshop on Mathematicians and School Mathematics Education was fantastic in bringing together a geographically and mathematically diverse group of individuals. In my specific case dealing with mathematics education as a tool of international development, the conference was a catalyst for a project to create a conference for finding donors for development projects and to coordinate a visit from participants from Paraguay and Chile to the Caribbean. These kinds of connections were facilitated by a conference as focused and international as this one. In a more unexpected way, the discussion topics outside of the panels and lectures provided a wonderful sharing of ideas such as how to increase the representation of women in mathematics and mechanisms for international cooperation. The logistical support and hospitality was excellent.

Mathematics, California State University, Fullerton

The workshop was very good. It helps me in my current researches allowing new collaborations with researchers from the SAT community. It gives me new insights and new ideas for my current research domain.

I find this particular kind of workshop very important and interesting. It purposely invited researchers from two disparate but quite related disciplines. It was very informative and stimulating to hear about the research conducted by our peers. Many thanks, once again, to BIRS, for allowing this special workshop to take place and a special thank you to the workshop organizers!

The workshop was an exciting and optimal mix of researchers from theory and practise. During the workshop I met with a number of previous, current, and what I hope will be future collaborators. One collaboration during the workshop led already to a paper, submitted to SAT'14. The workshop was definitely an excellent opportunity to get in contact with many researchers from the more applied side, whom I did not know before well.

The workshop was really inspiring in many regards, particularly it really helped bringing together the proof complexity and SAT solving community. It even lead to a nice joined paper with two other participants, which without the workshop would not have happened.

The talks at the workshop were very useful, offering deeper insights than would be possible at a conference. I embarked on possibly two new projects, while concerning my own projects I was able to start possible collaborations with at least three different groups. So I consider the workshop as very successful. On my own behalf, and on behalf of the two research communities involved.

My participation to this BIRS workshop had a very tangible outcome: while discussing with other participants, we discovered that we worked separately on a similar subject so we decided to team up to submit a paper to the next SAT conference (SAT14). I met during the workshop some people that I usually do not see or meet during conferences. It gave me another point of view of our research topic. I would say that the organization is close to perfect. I got a great time during the workshop, and felt home during the week. I could hardly believe that such a great place could exist. I am looking forward my next opportunity to attend a workshop in Banff.

The workshop was very useful in bringing together the complexity theorists with the practitioners to benefit future research in both domains. The organizers did an excellent job in putting together an agenda that enabled in-depth discussion on topics across the theory and practice spectrum. The discussions have sparked some new research ideas that I am exploring. In addition to meeting people who I had known of, but not met before, I met a few potential postdocs during the workshop that I will be in touch with.

Department of Electrical Engineering, Princeton University

The workshop was a rewarding experience. Well-planned and offering the possibility for interaction with many colleagues. BIRS is ideal for these kind of events.

That was quite an interesting experience. The research I am doing is highly theoretical (mathematical), and the workshop was a healthy mixture of practically-inclined complexity theorists and theoretically-inclined people from the SAT solving community. I was really impressed by the fact that understanding of the enormous challenges faced by this interdisciplinary area is quite similar, at least in some prominent circles within both communities, and I will try to get some students interested.

This was an extremely successful workshop that brought together two groups that typically do not interact. I believe it has created a dynamic that will foster future collaboration between members of the two groups. We should repeat this. The informal setting at BIRS and the extensive "face time" throughout the week (talks, open discussion evening sessions, meals, hike, etc.) made it easy for participants to engage in unexpected conversations. I certainly left with a new idea and am pursuing it with two other participants!

EECS/CSE, University of Michigan

This was a great workshop, where theorists and practictioners of Satisfiability solving got to meet each other, and explain their most recent results and open problems to each other. It was the most successful "bridging" workshop that I've attended so far. I've learned a lot about the practice of Satisfiability solving, and have found a number of interesting and well-motivated theoretical problems to keep me occupied in the near future!

From my point of view the workshop was very successful. It brought together people from two communities -the theoreticians and the more practical researchers- working in the area of satisfiability and the result was that we all were pushed out of our comfort zone and were exposed to many results and methods we were not familiar with. This for sure will influence my research in the future. The logistics, facilities and hospitality were all excellent.

The workshop I attended, Theoretical Foundations of Applied SAT Solving, exposed me in depth to material that I only knew about peripherally, and led to several new insights and new research ideas. I met and talked to several new people in some depth about their research. The facilities and staff at BIRS were the best I ever experienced at a professional meeting.

Computer Science, SOE-3, University of California Santa Cruz

This was a very impressive workshop that was directly relevant to my current research into the structure of string theory. I was particularly interested in the talks about the (2,0) supersymmetric string theory, which brought me up to date in a subject that would otherwise be difficult to come to grips with. The style of the workshop - its size, informality and schedule - together with the atmosphere at the Banff Center were ideal.

DAMTP, Cambridge University

It was indeed an enormous pleasure for all of us to organise and participate in this workshop. We were able to attract outstanding speakers and this helped ensure the scientific quality of the meeting. This is my second time at Banff and, as before, I'm amazed at the efficient way in which BIRS functions (not to mention the recent addition of a superb, almost magical, video-recording facility!).

The workshop was just fantastic in every possible way!

I was very happy to learn various new works on aspects of M-theory and related topics. To raise one example, I was able to grasp the idea of using 5D SYM theory to describe 6D (2,0) theory, its problem associated with the UV property of 5d SYM theory, the idea that the instanton modes may cire the problem. I was also able to meet and work directly with Stefano Kovacs who is on the other side of the earth (I am working in Japan and he is working in Ireland). This worked as a big stimulus to our project on the matrix model of M-theory. Stefano had gave a talk on a work with me, and I hope some participants get interested in the direction we have studied in the work.

Okayama Institute for Quantum Physics

The participation in the workshop was extremally useful for me. During the talks and discussions I have got many new ideas and also answers to questions and issues I encountered with in the course of working on certain projects. Unexpected relations between a priori different topics have been revealed which may stimulate new projects and collaborations.

INFN Padova

I had started a collaboration with one of the organizers, Ailana Fraser three years ago. But since we have not had contacts except for a brief one at Stanford in 2011, our collaboration came to a standstill. However, during this period of the workshop we were able to find time to discuss deeply about our project, and fortunately we succeeded in making a considerable progress! We are planning to continue the collaboration through Skype. I found a talk by Philippe Castillon very interesting, and so I will try to read his paper carefully and check if his result will be helpful for my research which is relevant with his.

Mathematics, KIAS

The workshop was great. The selection of the topics and of the participant have been done in such a way that all people could communicate and discuss with all the others. I personally started to collaborate with two people I had never personally met before.

It has been a great experience: great talks, inspiring and stimulating atmosphere and wonderful place.

Mathematics, ETH

This is a very exciting workshop. I got updates and new ideas that are extremely valuable to several of my current research projects. I also discussed possible collaborations with several participants of this workshop.

This was an extremely productive conference, I was able to hear about many of the latest research areas of my field.

Courant Institute, New York University

The BIRS workshop will have a significant impact in my research: several interesting ideas and insights were discussed and raised during the workshop that I intend to explore in the years to come. Moreover, we formed a working group during the workshop to discuss a particular subject in the area, and the result of this working group already led to a paper submission to an international workshop. As usual in this kind of events, I met new researchers in the area, some of whom I intend to collaborate in the future.

For me the main result of this conference was getting a chance to go through the formalisms that were being used by other practitioners in this space and relate them to my own. This forced me to put my current research into a more formal vocabulary, which exposed immediate connections to the work of other attendees.

S&P Capital IQ, McGraw Hill Financial

The BIRS workshop I attended provided a superb opportunity to meet new colleagues and work collaboratively in a setting that allows, indeed encourages, intense concentration. During the workshop, a longstanding co-author and I were able nearly to complete an article that has been awaiting time for us to collaborate in person. Even more important for me was the chance to meet in person a number of researchers whose research I have been following closely. More generally, the workshop allowed researchers from the several subareas of the rapidly developing Bidirectional Transformations community to get an up-to-date overview of the whole subject. Extremely valuable for everyone involved and for the subject.

Mathematics and Computer SCience, Mount Allison University

Helped me form a better picture of the current context and state of the research in this area, which is closely related to my research interests. Provided me with some questions to look into and potential areas of future research interest, although I need more time! It also clarified in my mind what my current MSc student should be looking into. The meeting provided me with a valuable opportunity to make some new contacts, and renew other contacts. It also allowed me speak confidentially with colleagues who have had contact with a potential future pdf candidate. Altogether I really valued and appreciated this opportunity.

It is wonderful to spend a few careless, focussed days in relative isolation with a nice, small group of people. These few days at BIRS I experienced the serendipitous atmosphere that works so inexplicably good in science. The organisers made the fantastic choice to reduce the number of talks and leave a lot of free time for discussion. For me, this turned out to be the best part: the naturalness with which small teams would form and let their thoughts flow, spending time together in the small discussion rooms; I was in at least one of those every day, and most of these discussions I expect will lead to new collaborations and definite insights.

As a PhD student (in number theory) I have only recently started studying operator algebras. It was very enlightening to hear more about how these structures can be used (in a number theoretic setting) in more generality. I have met many people with whom I have had interesting discussions. Hopefully I could also discuss things with them, once I am further along in my project.

This was a very interesting meeting and gave me ample opportunity to talk to experts in the field as well as getting to know what is happening in the field right now. These two aspects were most important for me. Organizers did a superb job.

Mathematics, University of Western Ontario

I found the workshop very interesting and informative. It did indeed help my research directly, since it brought together a team of 4 researchers with whom I have several ongoing projects. One feature of this workshop was that it was very well organised: the order of the talks was planned so that later ones could build on earlier ones. I also enjoyed the half-workshop format: it was easy to get to know all 21 participants. (I think this is probably especially beneficial for younger people, of whom there were quite a few.)

The workshop was extremely beneficial and stimulating. The program of talks was excellent, and introduced me to a number of exciting new ideas in number theory and dynamics that are closely related to my own area of operator algebras. A few specific benefits of the workshop were: * The intensive research environment and excellent breakout rooms enabled me to interact with collaborators to make significant progress on three separate research projects. * A number of the talks suggested extremely interesting connections with the theory of number theory and semigroups that are likely to lead to new research projects and new collaborations. * The workshop introduced me to new research contacts, both amongst high-profile established researchers, and amongst exciting current students who will be a part of the next generation of researchers in the area. * The workshop was extremely valuable for at least one current post-doc in my department; attendance and the opportunity to speak will have had a very positive effect on his job prospects. All in all the meeting was extremely well organised and scientifically stimulating and struck an excellent balance between interesting talks, and time and space for research interaction.

Thanks to you for all the attention! My participation at BIRS workshop was very useful and inspiring in the sense that allow me to aim new projects in related areas of mine. The workshop was very innovative in the areas that was covered, so all the on going projects actually are focusing in a most wide point of view. So the workshop was very interesting and useful for me. Thanks a lot!

Cientific and applied Computation Laboratory, Facultad Politécnica

As one of the organizers, I found the experience working with the BIRS team to be one of the best I've ever had in my career. Both prior to the meeting and on site, they are the best. Our program appeared to work very well, thanks to the extraordinary contributions of all the participants, both speakers and those who did not but contributed with their questions and round the clock discussions. New understanding of ongoing research questions, a sharper understanding of many outstanding problems, and the generation of some new questions were balanced against subgroups working on continuing collaborations. It was a great experience for my postdoc as it was for me. This multidisciplinary interaction has had impacts in all these disciplines and we expect to see more in the future making bridges between a good number of junior researchers for whom this was their first experience with this sort of workshop.

Mathematics, University of California, Santa Barbara

This was extremely good meeting. The knotted proteins are very interesting area of the research. For that reason, we had almost 100% attendance on all session - something very infrequent even when there is -20C outside. I would also like to praise Linda for all her efforts.

I think the workshop I attended was very interesting and high quality. BIRS facilities are excellent (my room in Corbet Hall a bit too cold). Overall, big success.

Dip.to di Fisica, Universita' di Napoli

I attended this workshop/conference as someone only marginally involved in the field, and was impressed at the level of collegiality between the participants. There were no disputes that I could recall, and everyone was impressively friendly. Any competition between the participants was hard to detect; there were certainly no egos on display. Overall a great learning atmosphere- I had a great time. Kudos to the organizers!

Physics and Astronomy, University of British Columbia

As usual, this BIRS meeting was excellent--great location, great food, great science. I did indeed have a fresh insight into how the mathematics of DNA recombination can be directly applied to reconnection events of vortex tubes in fluid mechanics. One of those eureka moments during a talk on DNA recombination by Mariel Vazquez at the BIRS meeting.

I have been a participant at quite a few BIRS workshops and they are always stimulating, interesting and useful. Every time I visit I renew my acquaintance with people with research interests close to mine and meet new people in more disparate parts of the subject. On this occasion I spent quite a lot of time talking to three of my collaborators about research problems -- e-mail might work well but it's hard to beat a face to face conversation and a blackboard! In addition I learned a lot about entanglements in proteins, an area about which I had known rather little before this workshop.

I learned a number of new ideas that will be helpful in my work as a curriculum developer and teacher trainer I met some wonderful people, who could be potential collaborators in the future

Gordon Hamilton and James Tanton put together a wonderful Unsolved K-12 conference. I feel that identifying 13 unsolved math problems that can be shared with K-12 students will be tremendously beneficial. I enjoyed being part of this event!

Riverbend Community Math Center

The Unsolved K-12 Workshop was incredibly stimulating for my professional life. It has advanced me professionally and academically in profound ways. It has expanded my knowledge of unsolved problems in mathematics, inspired me to work with teachers to disseminate and implement these problems in their classrooms, networked me to the colleagues in the discipline that I can now draw upon for information / wisdom / experience. I thank the organizers, Gordon Hamilton and James Tanton for inviting me and for providing such inspiring environment for this work. I love the conference booklet that Gord had put together!

I would sincerely like to thank and commend you for one of the most productful workshops I have attended. The workshop most definitely impacted my work and helped me to refine my creative science and math writing skills. The prominent participators in the workshop contributed to my professionality, as I hope my skills in digital creative writing in science and mathematics contributed to theirs. As a result of the workshop, I have already started to study the interaction between mathematics and poetry, a field which I most definitely would not have dreamt to enter had I not had the opportunity to meet the inspiring individuals that I met at the BIRS workshop. The workshop has inspired me to further deepen the knowledge, research and innovation in the interdisciplinary fields of creative writing and mathematics at our institute and I intend to hold local lectures, day workshops and perhaps even a weinar or conference on the topic. Once again many, many thanks.

I took part in the BIRS workshop on Creative Writing in Mathematics and Science. I had never written a novel before. For the past two years I'd been working on one about a mathematician -- a German refugee in the United States -- who disappears suddenly many years after the war, and whose disappearance intrigues a young mathematician who tries to discover its causes. After she learns about his life in Germany and what happened to him there before he managed to get to the States, she hits a dead end and is forced to give up the search. But then a memoir he has penned turns up and explains all. The memoir, which forms the largest part of the book, is both a bildungsroman and an account of a mission to spy on the American scientific establishment before and during World War II. In it, a number of real-life figures -- among them Admiral Wilhelm Canaris, Professor Felix Hausdorff, and Professor Emil Artin -- play important roles. The comments I received from the various participants, both about the novel's plot and about the chapter I presented, were immensely helpful to me in delineating the aspects of my writing that I have to clarify, expand, and edit. Several participants were sufficiently interested in what they saw and heard to ask me to send them the entire draft, and I now eagerly await their critical comments.

Mathematics, City College, City University of New York

I am a mathematician by training, but am currently spending my creative time writing poetry and blogging on the topic, "Intersections -- Poetry with Mathematics." I brought to Banff the beginnings of a poetry project -- I wish to develop a collection of verses that will focus on the properties of prime numbers and will convey to poets and other non-mathematicians the beauty and poetry of mathematics. Discussions with colleagues at BIRS helped me to see the strengths and weaknesses of my work-in-progress; they also suggested sources to tap for new ideas and directions for possible expansion of the original project-idea. For me a valuable week, a source of enrichment for the weeks and months to come! Thank you!

I enjoyed the camaraderie and the intense atmosphere at BIRS. We had a very successful workshop, where each of us learned from one another. I was able to make substantial progress on a current manuscript and I left Banff with new ideas for how to revive an older project. Overall this has been an excellent opportunity for me. I met some old colleagues and made new connections with very interesting people. In terms of facilities and such, things went very smoothly. I was sad that the exercise facilities are not in Corbett Hall but it makes sense I suppose. The facilities were perfect otherwise. The food was great, the rooms were comfortable, and the conference room was convenient. I hope to one day lead a workshop at Banff myself (together with my philosopher colleague Emily Grosholz) on humanistic (aesthetic, historical, philosophical, literary) aspects of mathematics. This workshop will be a good model for us.

In addition to congratulating the organizers, I want to thank you and your superb team at BIRS. They are outstanding. The workshop was extremely successful for me in many ways, probably the best workshop I have been to this year (out of 4). The scientific highlights for me were (a) new contacts with researchers in probability and statistics and the insight that I can incorporate many aspects of their presentations into my work; (b) new contact with one researcher in conservation ecology and the prospective of long term collaboration; (c) continuing work with existing collaborators on at least three projects. Thank you so much.

I came to the BIRS creative writing in mathematics and science workshop with a fictional work about an ambitious high school senior in the South Bronx, her progressive math class, and her mentors. It is a story built from a few solvable mathematical riddles, and loosely based on a true-life story. An excerpt (a half-dozen of the 47 chapters) circulated in advance of the workshop led to many valued intelligent conversations, discussions, opinions, and constructive ideas that could not have happened without the intelligence and collegiality of our wonderfully eclectic group of entirely egoless participants, all eager to hear and to know more about each other’s projects. Several perceptive ideas for improvements came during the time of my workshop presentation, and others came as residual ongoing discussions, sometimes late into the evening. I believe that everyone gained hugely from the wisdom of our wonderful group. In speaking with others, I understand that the whole event was an outstanding success, and that everyone felt both a sense of accomplishment and an awareness of work to be done. I am a nonfiction author, in particular, an author of narrative popular mathematics. The work I presented at the workshop is my untrained attempt at putting together a work of fiction incorporating narrative mathematics skills. With one whole week devoted to critiques in writing, I came away with a comfortable list of ideas for improvements and an exhilarating sense of accomplishment, a feeling that would be hard to come by in my usual world of solitary writing.

I was thrilled when I received the invitation. Now that the workshop is over, I realize how lucky I was to be part of it. I had the opportunity to meet a wonderful group of writers/scientists and to benefit from their expertise. In particular, I highly appreciated their comments and constructive critique of the two pieces I submitted, and their advice as to possible venues for their publication. I'd like to believe that in a small way I also contributed to the success of the workshop by leading a discussion on the use of fiction to communicate mathematical, and more generally scientific, concepts and results to a wide audience. I wish to thank again Marjorie and Florin for inviting me to BIRS. I had a wonderful time, and not only on the professional front.

The workshop was amazing. Thank you so much. It was the first time, as far as I know, that there was a workshop devoted to the mathematics of cyclic populations, and it turned out to be an extremely good topic: It was focussed enough, so that everyone was interested in everyone else's talks, but rich enough to generate an enormous variety of mathematical approaches and ingenious experimental designs. In addition, the group gelled beautifully, and the discussion sessions were lively and very interesting. I am quite confident that the paper we started writing during the workshop will actually get finished. There is more about the paper in the report, which I hope to submit by the end of the week (it's written - I just need approval from my co-organisers).

It was such a splendid workshop of the size which make the communications and discussions with top active researchers in the field much more effective.

The igtc summit is a fantastic networking opportunity. The focus on students throughout the weekend makes it one of the most important events of the year and does a lot for student employability and research enthusiasm. As this workshop is at the edge of my field, I learned a lot, especially since it was very accessible. From these summits and the igtc program in general I am a much better supervisor because of its strong emphasis on providing students with opportunities and the goal of reaching out to a broader audience for collaboration and networking.

Department of Statistics and Actuarial Science, Simon Fraser University

Participating in this BIRS workshop has been a very positive experience. The variety of research presented by the students and faculty was extremely informative and interesting. Also, the possibility for discussions between students and IGTC faculty gave me valuable insight into problems on which I am currently working. I also found this to be a great networking opportunity, especially at the current stage of my degree. Two of the faculty members at the workshop offered to let me know about any post-doctoral positions that might become available in the next year. Also, the career component of the workshop was excellent, and very relevant for all the students.

This was a fantastic workshop that allowed me and my students to network and to find out about important research being carried out by other Math-Biology groups in the PIMS geographic region. We found an important and direct link between the research on breast cancer done in my group and that of another group in Edmonton (Ton Hillen), something we were not previously aware of. As a result, my student has been invited to visit the other group, and some mutually beneficial collaboration may result. We have already discussed comparing two distinct ways of modeling the same scenario, which would allow for direct comparison of methods used in the field of 3D cell interaction computations (Cellular Potts Model versus Deformable Ellipsoid model). This is something I had always wanted to be able to do, and is possible for the first time now. Aside from benefit to my own research, the workshop was of exceptional interest and quality as far as student presentations, career planning, and quality of advice for finding positions and planning for the future. I am very very glad I got to go to this workshop, and I hope it will be repeated in the future. In my mind, this is one of the best investments in young scientists that we can make, at relatively reasonable cost in terms of time, funding, and resources.

Mathematics, University of British Columbia

It was great fun and learning experience. I had chance to meet new students with range of background. It was nice to discuss my research work problems with other students and faculty members to have better suggestions/recommendations that are helpful for me. Simply, it was awesome!

The workshop was a way of getting acquainted with topics that are currently outside of my comfort zone, as well as present my own research to people working in diverse fields. In that respect, this may well prove to be a catalyst to many new projects. I can testify that I did meet a lot of new people, some of whose work I find extremely interesting and germane to my own work. Since I am a graduate student expecting to finish within a year, I hope I made a suitable impression on the many people I met here. I feel I can provide new tools and techniques to certain problems they are interested in, or I can work on a slew of different problems that may have unexpected connections to their research. For example, cancer genomics now goes hand in hand with the understanding of the spread of cancer, and epidemiologists often look to genomic indicators for the spread of the disease. From the point of view of my favourite discipline, being a more theoretically oriented person, I do not think the workshop had an impact on my understanding of the concepts I am interested in, but the whole point was to understand something new, and I believe that the workshop excelled at this goal.

Department of Mathematics, Simon Fraser University

This IGTC workshop was geared towards graduate students in math biology, and as such proved to be excellent. The training sessions certainly helped my students' careers and exposed them to different views and different career paths. The poster session gave them feedback from researchers and students and created lots of discussion and energy. The talks exposed them to different topics and gave insight as to how modern mathematics is being used to model biological systems. In addition, I learned about models being developed by other researchers in math biology, and found out about some papers in the literature. These may help with my research projects. I also witnessed the enthusiasm and talent of this group of students.

First, thanks for the organizers' supporting me to attending such a nice workshop and present my research to colleagues. I learned a lot from this workshop. I got to know a lot more related research topics that interest me from the talks and posters from other colleagues. I also got a variety of good suggestions from the senior researchers on how to balance the life and research, how to adjust myself to future academic life. Meanwhile, I made a lot of friends with graduate students and enjoyed that wonderful talks. Finally, I had a more practical expectation of my future career after listening to the record of new faculty who were IGTC graduate students. Thanks to Dr. Daniel Coombs' perfect organization of this summit and personal suggestion to me. By the way, the accommodation is really splendid!

Since this was a very focused mini workshop, each talk was interesting to me and will impact on my (and indirectly my students') research. Of course, there was also a bit of networking, both advertising my department's students and postdocs and learning about such folks elsewhere. Together with 3 others, I also proved a new result answering a published question.

Mathematics, University of Wisconsin--Madison

It was very nice to participate with other colleagues doing different kind of mathematics. I think everyone wanted to explain basics of their own work. The idea of having a small workshop is great since helps the participants to interact. I met postdoc students with whom I am going to colaborate.

Mathematics, Instituto de Ciencias Matemáticas. CSIC

The BIRS Workshop on Computable Model Theory was wonderful. The talks were good and it was incredibly helpful to have so many colleagues gathered together in one place. It is too early to tell where some of the research collaborations will lead, but it is certain that they would not have even started without the BIRS workshop. Thanks for all the work keeping BIRS running. It is a fantastic resource for the mathematical community.

It is my duty and pleasure to thank you for the very stimulating workshop I was invited to.

The workshop was great, it was an occasion to meet people that I heard about but never had seen before.

The workshop was very stimulating and hopefully will lead to new research. It was also very stimulating for my graduate student who attended it. I had previously organized two workshops at BIRS (2005 and 2009) and plan to organize more in the future.

Mathematics, University of California, Irvine

A super conference. A great meeting of substantive scientists and applied math specialists. Surely there will be both novel managerial methods and contributions to statistical science resulting. Keep doing what you are doing so well.

Department of Statistics, University of California, Berkeley

Thank you for the opportunity to respond regarding the BIRS workshop. I was a bit intimidated going to the workshop after reading the positions and backgrounds of most of the attendees. However, after attending the workshop I have to say that I have a new appreciation of the power and role advanced statistical analysis can have on every day programs and situations and the people who understand those methods. The presenters and attendees were all very down to earth people with great insights into methods of solving day to day problems that I found really fascinating. I have come away with some great contacts and appreciation of what Statistics can do in the everyday world. If ever I have the opportunity to attend another BIRS workshop, I would do so readily. My attitude towards, and understanding of statistics and mathematics as it relates to my everyday job and its challenges has changed. Thank you again for a enjoyable and educational workshop.

Environment and Sustainable Resource Development, Alberta Government

The use of quantitative methods for the management of fire on populated landscapes is my primary research interest, so I found this workshop to be highly relevant. The workshop was very well organized and featured a well thought out list of invitees. The participants were a nice mix of senior academics, early career researchers, post graduate students and fire agency personnel. The program contained a good mix of both prepared talks and discussion sessions. Participants approached the workshop in the true spirit of scientific inquiry, with exchanges of ideas and robust discussions and debates held throughout the week. As a direct result of the workshop I gained some new insights into problems I'm working on, made some new contacts and I expect I'll be involved in at least one new collaboration/paper.

The BIRS workshop on Managing Fire on Populated Landscapes was extremely useful for me. It led to some new insights that will help with my research. I will also be exploring two potential new studies arising from contacts made at the workshop.

I think this workshop was very exciting; it brought together people looking at Whittaker functions from many different points of view.

Department of Mathematics, Boston College

The workshop was a very useful continuation of a previous one this year at ICERM, by helping keep up the momentum in this area. I had the chance to present my work in a talk. I continued to learn several interesting things - I appreciate that the organizers took into account the topics on which I wanted to hear presentations. It was a good occasion to meet my collaborator, Anne Schilling, and continue a project with her.

Mathematics and Statistics, SUNY Albany

I was not so familiar with WMDS (Weyl group multiple Dirichlet series) before this workshop, and this program was particularly useful to learn the basic concept and techniques on this subject! It contributes for me to find connections to the theory of prehomogeneous vector space, which is my research topic. There are lots of time to talk freely, and such informal discussions were helpful also. In addition, my collaborator and I made a good progress on our joint project, which was invaluable.

My participation in the BIRS workshop impacted my current research in many ways. I enjoyed all talks in this workshop and got some new fresh insight.

It was an amazing experience for me. I gained a rough idea on what this area is about, what is their most concerned problems etc. I also got the chance to talk to professors and students from both statistics and oceanography fields and generate some interesting conversions. I also identified another two problems that we might attack in the future and maybe new connections.

Attending the workshop 'Geometric and topological graph theory (13w5091)' turned out as an excellent opportunity for scientific collaboration, as we managed both to initiate new collaborations as well as deepen the existing ones. In the latter regard, we had several exchanges on possible projects that could be submitted to various grant applications, as well as on completing the existing projects that are close to termination. Regarding the new collaborations, we discussed several open problems, and tested several approaches to them. With Radoslav Fulek, we investigated the gap of the crossing number additivity over cuts, with Jernej Rus, we devised a roadmap that will lead to an efficient algorithm for counting stable traces in graphs, and with Dan Archdeacon and Luis Goddyn we investigated approaches to formulating the thrackle existence problem as a stack of constraint satisfaction problems that may lead to a new algorithm for recognizing thrackle graphs. Besides the actual work, there were several interesting talks presenting deep, although sometimes counterintuitive new results.

This was an excellent workshop. I gave a talk on my most recent research project. I get several helpful comments, and made further progress on it. I also heard some wonderful talks by Kostochka and others on progress on some old problems on graph coloring, with very impressive results. I met a number of students (I knew almost all of the postdocs and faculty).

Firstly, I would like to thank all of the workshop participants and especially the organizers and Banff Centre staff who helped make the workshop productive and successful. Paul Seymour and I presented the following conjectures by Kalai and Meshulam: (1) If a graph has no induced cycles of length a multiple of 3, then the number of even independent sets minus the number of odd independent sets is at most one in absolute value (2) If a graph has no induced cycles of length a multiple of 3, then the graph has bounded chromatic number (and, as a stronger conjecture, is also 3-colorable) (3) If a graph has all of its induced subgraphs satisfying number of even independent sets minus number of odd independent sets is at most 1 in absolute value, then the graph has bounded chromatic number These conjectures generated much discussion, especially with Zhentao Li. Zhentao Li, Paul Seymour, and others, including myself, worked on adapting Matthew Plumettaz's results for graphs with no cycles of length a multiple of 3 to the dual problem of having no bonds with a multiple of 3 edges. We discussed how to prove that there is no simple, 3-edge-connected graph with no bonds having a multiple of 3 edges. Additionally, many of the presentations not only presented interesting problems to consider, they also provided possible approaches for proving the Kalai and Meshulam conjectures in whole or in part. I was able to meet with fellow workshop participants, who were friendly and eager to discuss graph theory both during the scheduled activities and outside of those activities; I look forward to having future discussions with them. The workshop was a very educational experience, one that I hope is a starting point for my future mathematical endeavors.

It was a great meeting. I learned not only excellent results, but whole new for me topics to study and use. One example is the talk of Jacob Fox, where I learned the topic of Turan-type problems for permutations, apart from his outstanding result solving (disproving) several old conjectures. Also I started a new project with Hehui Wu at the conference.

My participation in the BIRS workshop was excellent stimulus to my research. There were many exceptional high quality talks from Jacob Fox's talk about the new and exciting interval minors to Paul Seymour's talk on variants of Woodall's conjecture. Yet there were also many informal but equally enlightening conversations. In particular, I was able to discuss ongoing work with my colleague Zdenek Dvorak, to work on open problems with Sergey Norin, and to discuss career plans with many of the graduate students attending. Groups of us would sit around at night and tackle interesting open problems. While we were able to resolve a number of questions via our combined manpower, there were still a number left unresolved that caught our attention, for example Aharoni's conjecture that chromatic number of the union of two chordal graphs is at most the sum of the clique numbers. I am very pleased to have been so inspired.

It was a great workshop, there were many exciting talks, I would like to point out two of them. Jacob Fox's talk (Stanley-Wilf limits are typically exponential) was extremely interesting, just like the main result, it is really surprising that such elementary (but very tricky) methods work in this deep problem about matrices with forbidden submatrices. These results are strongly related to the theory of geometric and topological graphs. Radoslav Fulek's talk (Recent progress on Hill's conjecture) was also very interesting, he described a generalization of the methods and formula of Lov\'asz et. at. that connects crossing numbers and $k$-sets to monotone (and more general) drawings. I learned about many interesting new results, methods, ideas, from the talks and from discussions, and I hope I can use some of them in my own research.

Some of the presentations contained new ideas that both gave fresh insight to an old problem I had grown frustrated with and a new problem I had not considered before.

I really enjoyed most of the talks, some of them gave me new ideas, some gave new questions that I would like to study later in my research(f.e. Alex Scott's talk was really interesting for me, since it is close to my research area). Also, I worked during the workshop with Professor Alex Scott and Bruce Reed.

The conference brought together people from academia and government and in very diverse backgrounds - mathematical modeling of infectious disease and aboriginal / First Nations health researchers. I gained an enormous amount of insight into how these methods can be useful in the specific context of aboriginal health. I also met researchers and graduate students that I would never had had an opportunity to meet, and I think some of these contacts will be very useful in the future. Thank you very much for hosting this opportunity.

Thanks for your email. We had a wonderful time at BIRS and a very productive meeting. BIRS really is a beautiful facility. Thank you to you and your team for making the arrangements and for ensuring that the meeting ran smoothly. The food and accommodation were great and all of the participants seemed to really enjoy their stay. The only problem we encountered was with the A/V equipment. A macbook was left for us to use so that we could project presentations but the correct attachments to connect the macbook to the projector were not left for us. Luckily someone else had a Windows laptop and we used that.

I did really enjoy my time in Banff both for the atmosphere locale, food etc and for the content of our session. I learned a lot, made new professional connections, and developed some new ideas re research around indigenous health. I will be developing these with my colleagues and using them in my work in the future. I also thank Jianhong Wu, Seyed Moghadas, Michael Li and the others involved in organizing this workshop.

Thank you very much for your message and for your great efforts on governing BIRS. I greatly enjoyed the workshop, both the scientific part and excellent venue. The workshop provided a great opportunity for exchange in ideas and fruitful discussion, as well as for most pleasant personal interactions. All this is very valuable for my research program. I wish you all the best in carrying on your important mission of supporting research.

We found that BIRS was a wonderful and very well organized host for our workshop, in what was of course a very stimulating and beautiful environment. The workshop was very focused and went very well.

I just wanted to write to you personally to say how outstanding the BIRS facilities, staff and organization were for this event. I have held one workshop previously at BIRS in 2010 and it was a pleasure to have the opportunity to host again in 2013. I can honestly say that I don't know of a finer venue for such meetings, and hope to have the opportunity to host another BIRS workshop sometime in the future.

I certainly enjoyed the meeting and especially had some really productive conversations both with Ralf Schuetzhold ( which is not surprising since he is my former post doc and we are writing a book together, part of which we worked on while at BIRS-- it was great in that it gave us uninterrupted time to work together) and with M Hotta, whom I had met before but with whom I had some very stimulating and intense discussions, and we will probably be writing a paper together. So thanks again.

Thanks to Michael and Zongpeng for organising and to BIRS for setting up the stage for this exciting and intimate gathering. I am really glad to have attended this workshop. The workshop went very smoothly and we had some really good discussions. One of my favourite features about this setting was that we really got a chance to appreciate the intricacies involved each other's works, which is usually not possible in a much larger workshop or conference. I also got some new ideas and future directions for my own research based on the interactions we had.

Institute of Network Coding, Chinese University of Hong Kong

I really enjoyed the workshop, I had the opportunity to meaningfully interact with colleagues on a number of research problems in a great environment, thanks for making this possible!

This was a very nice workshop. I have got some new ideas from the presentations. Several excellent presentations were very inspiring. Also I got to know several people who work in this area and we might have further discussion in the future. Thanks to the BIRS and the hard working organizers who gave us the nice workshop.

The conference gave me a much better insight to my field. As a young graduate student I feel that I greatly benefited from following the talks and speaking with other participants. I made new friends and strengthened old relationships. These contacts may well lead to collaboration some day or help getting employed, but have not done so yet. The practical arrangements were excellent and I enjoyed my stay greatly.

It's been a pleasure organizing this workshop at BIRS. This is my first visit as a participant and as a organizer and I have to say that I was very impressed with the Research Station. The staff were really helpful (during the past two years) and the facilities were excellent. We have the feeling that the workshop went well and there was a good balance between talks and time for discussions, but we'll get a better feeling once we write out our report. Many thanks for the support, centers like this are invaluable for the profession.

The workshop I attended significantly broadened my knowledge of the field, gave me many new perspectives, and I got to know new people in the field with whom I may collaborate in the future. I hope to attend the next time this workshop will be held at BIRS. I strongly recommend the BIRS scientific board to consider making this a 5-day workshop where more people can be invited and longer talks can be held.

Racah Institute of Physics, Hebrew University of Jerusalem

An excellent meeting with great speakers!

This was a very fruitful meeting for me, and I think others, in discussing current research on a selective model in the Lambda coalescent. There was a particular section in a proof that needed working through that we managed to work out in the meeting and present to the audience. I did get a lot out of the meeting that firmed up research ideas. It was a great meeting in a great environment. I also went walking on an afternoon off through Cory pass with others.

The workshop was a very nice experience for me to keep up with the new development in my research fields.

The workshop gives me a chance to realize the application of the Poisson-Dirichlet distribution and Dirichlet process in Bayesian statistics, which is quite amazing.

This Workshop was a unique opportunity to meet top-level scholars in this field. As a researcher I gained a lot of insights in the discipline and several suggestions to pursue my research in many directions. Finally, the participation of several practitioners was also useful to my research in this field. Overall, it was a wonderful opportunity to develop new contacts and collaborations and to get new ideas on specific topics.

Mathematics, University of Bologna

The week long workshop gave me the opportunity to discuss my research area with regulators, practitioners, and researchers from other disciplines who broadly share my interests. It sparked quite a few new ideas and I thoroughly enjoyed the experience.

The scientific contents was focused on one theme, but very diverse in term on the participant backgrounds, scientific approaches, professional contexts (academic versus industry), or questions to be addressed. This very interesting balance leads to a steep learning curve for me, and to intense discussions. It was certainly a very enriching week, where I exchanges intensely with some colleagues, but also where I learned to understand and appreciate in depth other approaches used in the field. The week was also very interesting in term of the contacts made during the week, both in the academic circles and in the industry.

Great workshop!!! It will influence the direction of my research!

Geological Sciences, The University of Texas at El Paso

This is early to say something about the outcome, but we started a promising discussion with S. Shadrin in Banff. I think in general the workshop has been successful to exchange new ideas with the many participants, and get updated. Two years ago, I attended the workshop New Recursion Formulae and Integrablity for Calabi-Yau Spaces (11w5114) and after the talk of H. Fuji, the intense discussions with B. Eynard and M. Marino at the workshop have led two of us to propose a conjecture (arxiv:math-ph/1205.2261, submitted to Quantum Topology) concerning the asymptotics of the colored Jones polynomial of hyperbolic knots correcting and completing the work of Fuji et al.

Very well-organized workshop in beautiful environment. Will affect my work as PostDoc with one of the organizers.

I benefited a lot from the lectures and discussions with the workshop participants. I will see if some of the ideas I had during the workshop can be made into real research projects.

The workshop in Banff on Integrable systems and Moduli spaces was extremely fruitful. And the services offered by BIRS was impeccable. Through you I would like to thank BIRS for extending all out supports to make the workshop successful.

My participation in the BIRS workshop impacted my research in the way that discussions and feedback from my talk helped me understand things around my research much better. I have also learned a few fresh ideas on the cohomology of moduli spaces, as well as gained a much better understanding of their relation to integrable systems.

School of Mathematics, University of Minnesota

My participation in the WIT workshop had had and will continue to have a strong impact on my current research. Our team was more productive than I would have dared to dream it could be. This new collaboration will lead to the submission of at least two articles in the near future, of which one to the workshop proceedings, and we fully intend to continue collaborating over the next few years, as we have numerous exciting ideas for extensions of our project. It was altogether an amazing week, professionally and personally.

MATHGEOM, Ecole Polytechnique Federale de Lausanne

My participation in the BIRS workshop had an impact on my current research and allowed me to get a fresh insight into some aspects of my thesis. I was happy to meet some new and old colleagues there, from whom I learned new things, useful to me. The workshop week was very productive and fantastic!

The WIT workshop was extremely productive and I am still amazed of what we all managed to do in just four (long) days. I admit that I was sceptical about the concept, but it worked! Our team plans to submit a paper to the workshop proceedings and I am sure that we will continue our joint work in the future. It was a great opportunity to meet women in topology and the atmosphere at BIRS was really inspiring. The workshop was also the starting point for a 'Women in Topology' network. I hope and expect that this will in particular help young women in the field.

Department of Mathematics, University of Hamburg

This was the most productive workshop I've attended in my career. We went from a few half-baked ideas to enough material for a research paper over the span of four (albeit rather long) days. I now have new collaborators with whom I'm eager to work in the future. I expect this week to pay dividends for a long time.

Mathematics, Harvard University

I have no hesitation to say that the WIT workshop was the best and most successful and productive mathematical event that I have ever attended, and here is why: - One of the workshop's goals was to forge collaborations between women in topology, and it has been accomplished. In my case (and I believe many others too), the collaboration will be continuing well beyond the scope of the workshop. - The collaborative project that I participated in during the WIT workshop was my initiation into a subfield of homotopy theory that I had not previously worked in. As a consequence, my research has been significantly broadened, which is yet to positively influence my career. - My team obtained significant new results that will be written in two research papers. - Our results will be a basis for follow up research projects. - The atmosphere of the workshop was more friendly and supportive than most math meetings I've attended. - The evening discussion groups on issues of concerns to women in math/topology were extremely helpful, especially for us younger mathematicians. - As a result of these discussions, a network of women in topology is being formed as a forum to continue the support and collaboration of the WIT workshop.

This was an excellent event. It certainly had an impact on my research and I expect the effects to continue for a long time. In the short term, our research team involves me with three new junior collaborators. We expect to submit a research article to the conference proceedings. We have also discussed possible future meetings of our team and plans for possible longer term projects. The meeting marks the start of an international Women in Topology network. This will be an excellent contribution to supporting young women in the field. For me the meeting was a great opportunity to get to know many of the younger women. I expect it might have an indirect effect on future hiring, in that I will now be aware of potential applicants I might otherwise not have known of. The workshop was a very positive experience for all involved, I think. I very much look forward to future Women in Topology events.

School of Mathematics and Statistics, University of Sheffield

The workshop had a great balance of biology and statistical components. The mix of people from different fields contributed to interesting and fruitful discussions during and between sessions. I made new contacts and deepened existing ones. The week also made it possible to move one of my long-term projects forward thanks to one of the other participants. The BIRS workshop with approx 40 people is by far the best setup for network, discussions and scientific creativity that I've ever experienced.

Epidemiology and Biostatistics, University of California San Francisco

The workshop assembled some of the most excellent researchers in my field - statistical aspects of genomics, gene regulatory networks, personalized medicine. Talks and the informal interactions during breaks, meals and outdoor activities were extremely stimulating. A number of ideas were exchanged that are likely to affect the future path of our research.

I was very happy with the scientific content of the workshop. The program was particularly well designed, featuring several talented researchers in my field and in connected fields, some of whom I didn't know and will now have a chance to get more familiar with their work.

The BIRS meeting was my first, and I totally enjoyed the experience. The workshop attracted some of the most prestigious and productive scientists in the field as speakers. I got to catch up with many colleagues, and got to make many new friends. The talks are great, the facilities and services are very nice, the environment helps participants socialize. I might be collaborating with Benjamin Haibe-Kains, and during another talk I thought of a good project to try out at my home institution. I would recommend the BIRS conference to anyone in my field, and would love to come back again.

Biostatistics and Computational Biology, Dana-Farber Cancer Institute and Harvard School of Public Health

This is my first BIRs and it was stellar. Not only did I learn a lot that has helped my research program but two specific collaborations have emerged. One is the application of a Bayesian effect size shrinkage approach to a family genetics studies we currently have been writing up. The other is a statistical model for analysis of differentially expressed genes from high-throughput RNA-sequencing data. Both have advance our ability to analyze complex and high-throughput RNA sequencing data.

I am writing to express my great appreciation to BIRS for hosting the recent workshop on regulatory networks and personalized medicine. The workshop was exceptionally well organized and featured numerous engaging presentations. My own research has already benefitted significantly: following my talk a participant informed me of his previous development of (an obscure) constrained optimization algorithm that is ideally suited to the problem (genome reconstruction) I was exploring. Moreover, another talk detailed methodology (network deconvolution) that dovetails nicely with, and potentially greatly expands, a student's doctoral thesis. I had several informal interactions -- readily facilitated by the fabulous setting -- that I believe will also enrich my research. So, thanks to you and BIRS for enabling a wonderful and fruitful experience.

The BIRS workshop has been very informative. I got to know many cutting edge works, which definitely will have good impact in my own research. I also got to know in person other participants in the workshop, and could potentially form valuable collaboration with them in the future. I talked with quite some students and postdocs in the workshop. I will be happy to hire some of them if they are interested in joining my group later.

The workshop was very useful. Considerable number of personal discussions with different participants was fruitful for my own research.

Institut de Mathématiques et de Modélisation, Universite de Montpellier II

Many thanks for the chance of organizing the BIRS workshop of "Inexact Optimization Theory for Resources and Environmental Management" (13w2178). It was very successful.

The workshop provided me with a lot of fresh insight and alerted me to some new and exciting results in the area. The selection of speakers was excellent! Several ideas for new projects came to my mind after listening to the talks.

This workshop is the third in a series on related topis (the first two took place in 2005 at AIM in Paolo Alto, and in 2009 at the MFO Oberwolfach. What has made these workshops particularly interesting is that they have been very focused (on eigenvalue problems), yet have attracted researcher across several disciplines, most notably Mathematical Physics, Spectral Geometry, Functional Analysis and Convexity. I am particularly interested in the "ovals conjecture", which says that a certain geometric eigenvalue problem involving the curvature of a loop should assume its minimum at the circle. Significant progress on this conjecture was reported at both subsequent workshops. This time. Jochen Denzler showed that the problem has a solution given by a planar, convex, smooth curve with strictly positive curvature. This problem continues to intrigue me, and the above meeting at BIRS was the ideal place to discuss it. I hope to see a resolution in the coming years ! The community is especially welcoming to younger researchers and students, including several Canadians who have recently returned to the country. Sadly, a number of researchers from abroad were affected by the visa strike and could not attend.

The workshop gathered together some of the leading researchers in this area and I found it quite profitable to learn about the most recent results, as well as being able to discuss future directions with some of the participants. It is too early to say whether or not these will translate themselves into actual publications, but definitely the overall balance in this respect is quite positive. It is not possible to follow all the developments and publications in this area, so I believe that the workshop was quite useful in giving an overall view of what is going on, which of course also shapes future developments. Workshops are always useful to discuss the work of your students and postdocs with other researchers, finding out about positions, etc, and this one was no exception.

Although I knew the majority of the participants already, there were several valuable new contacts. In particular, new ideas for research directions grew out of discussions with Alessandro Savo and Lotfi Hermi, and the open problem sessions were thought-provoking. I am not currently either seeking a job or involved in hiring, but it could make a difference in future hiring that I met some bright young people in spectral theory.

At the BIRS program 13w5059, I reported on the work that originated in discussions at the 2010 BIRS workshop 10w5106; additional progress was achieved at a 2012 workshop 12w5072. This resulted in two publications: 1) Y. Canzani, D. Jakobson, R. Gover and R. Ponge. "Conformal invariants from nodal sets." pdf, arxiv:1208.3040. To appear in IMRN; 2) Nullspaces of Conformally Invariant Operators. Applications to Q_k-curvature." pdf, arxiv:1206.0517, published online in Electronic Research Announcements in Mathematical Sciences, Vol. 20 (2013), pp. 43-50. I am also involved in several projects extending those results. At the BIRS program 13w5040, I reported on a series of projects that were discussed at the workshop 09w5040. These projects resulted in 3 publications: 1) Y. Canzani, D. Jakobson and I. Wigman. "Scalar curvature and Q-curvature of random metrics." To appear in Journal of Geometric Analysis. DOI 10.1007/s12220-013-9406-9; 2) Short announcement: Electronic Research announcements in Mathematical Sciences, Volume 17, 2010, pp. 43-56. 3) L. Chen and D. Jakobson. "Gaussian free fields and KPZ relation in R^4." arxiv:1210.8051, to appear in Annales de l'institut Henri Poincare. Another project is nearing completion, and a series of related projects have been completed (Y. Canzani, D. Jakobson and J. Toth. "On the distribution of propagated Schrodinger eigenfunctions." arxiv:1210.4499, to appear in Journal of Spectral Theory), or are in progress.

Mathematics and Statistics, McGill University

The workshop was a great success for me! I met two collaborators with whom I could work intensely. I also met other people I know and could discuss with them. I met young people I did not know which was also very interesting for me. Certainly the workshop was very inspiring for me! The talks and discussions gave me new ideas.

Department of Mathematics, Universitaet Bielefeld

I made new contacts with people I hadn't met before. Some of the talks were very inspiring for me, and in fact, I now have a new idea of a whole (rather big) project based on some of the talks and discussions I had afterwards. I also continued some of my ongoing research projects with people I hadn't seen in a while. And perhaps most interestingly, the environment is really inspiring too: on one of the nice afternoon hikes we had, we started talking about mathematical ideas, and it turned out that our research had connections we weren't aware of before.

Department of Mathematics, Ghent University

Thank you very much again for your hospitality during this workshop. We enjoyed a great scientific program which nevertheless left enough time for working on research projects with the colleagues. During this workshop Kay (Magaard) and I have been working on a sequel of our paper "Imprimitive irreducible modules for finite quasisimple groups". The objective is to complete the classification for quasisimple groups in characteristic 0. In our first paper we had to assume that the groups of Lie type arise from algebraic groups with connected centers. This assumption excludes certain quasisimple groups. I was also invited to give a talk on recently completed work with Husen and Magaard. Apart from the scientific actitivities, I enjoyed the inimitable location of BIRS, and in particular the delicious food offered. Thank you once again for inviting me.

I did already send details on my scientific interaction with other participants to the organizers of the conference. I got to know several young participants which might facilitate future hiring decision.

While at the workshop I was able to finish one joint paper (with other participants) and start on a new collaboration. The workshop also benefited me by drawing world-class algebraists to Alberta, some of whom agreed to extend their travels to visit me in Lethbridge. This has been a great boon to my research.

We had long chats with Zinovy Reichstein . His favourite area (the subject of his recent ICM talk) is essential dimension of various structures. It seems that I will be able to prove some new results about the asymptotic structure of finite groups(my favourite area) with given essential dimension. With James Wilson we discussed possible joint work elaborating a connection I found between permutation groups (the subject of the workshop) and p-groups (his favourite subject).

The workshop was excellent. I now have at least three new collaborative broad research projects to work on, possibly more.

Joy Morris, Pablo Spiga and I spent quite some time at BIRS working on the problem of proving that almost all Cayley graphs on generalised dicyclic groups are graphical regular representations. We made significant progress and it looks like we will submit a paper based on this research later this year. I also had some interesting discussions with László Pyber about related topics.

Participation in the BIRS workshop on Permutation Groups introduced me to ideas and new contacts that could benefit my research. Although at an early stage and there is nothing concrete to report at present, there is the possibility that papers and new collaborations could emerge from the meeting. My research in topological groups has links with permutation groups and algebraic groups, which were the main focus of the workshop, and two of the talks described ideas that might transfer to solve particular problems concerning topological groups. I will explore both these ideas in future work. Although broader and less specific, insights gained in other talks were also beneficial. I had useful discussions with several people. In some cases these consolidated links that had been initiated previously but in at least two other cases were new links that could lead to new collaborations. I met and heard talks by a number of younger mathematicians in fields related to mine, who I will keep in mind when advertising positions in future.

Mathematical and Physical Sciences, Newcastle Australia

The workshop was fantastic, and I am deeply indebted to the organizers and BIRS for making it so successful. Being quite young in my career, the opportunity to interact mathematically and socially with the other participants, being of all different levels, was great, and I will likely not realize all of the impact for many years. That said, here are some concrete anecdotes: 1) I spent a few hours discussing some aspects of Moufang sets with Tom De Medts and Yoav Segev. There are some configurations that have come up in my research on which I am hoping that they may have some insight. The problem did not get solved, but we shall see. 2) I spoke with Dennis Gulko about his research on linear sharply 2-transitive groups. I was especially excited that his approach made use of the notion of generic 2-transitivity, a topic on which I have been thinking and which was the subject of my talk at the workshop. He is interested in extending his work to linear sharply 3-transitive groups, and we talked a bit on how one might get started. 3) After speaking with Dennis about his work on linear permutation groups, it seemed to me that it would be quite interesting to investigate linear Moufang sets. I believe that the general theory might be able to be considerably sharpened when restricting to the linear case, and perhaps, in a way analogous to Gulko's work, one might be led to consider some generic version of a Moufang set. I mentioned these ideas to De Medts and Segev, and they agreed that these would be interesting to explore. 4) Following my talk, I received some comments from Bob Guralnick and Zinovy Reichstein on a problem I mentioned about degrees of generic transitivity of simple algebraic groups, and I plan to follow-up with them in the near future. Again, I am so happy to have been a part of such an enjoyable workshop. Many thanks to all those that made it possible.

It was a great meeting in a wonderful setting. I benefited a lot from many discussions with several prominent colleagues - a few for the first time. But also it gave me the opportunity to interact with several young researchers, which I found to be rewarding.

An interesting link was discovered at the workshop during the discussion following the talk of Reidun Twarock. During her lecture she explained that the structures of the capsids of numerous animal viruses, including not only the overall icosahedral structure but also the detailed structure of the subunits, could be understood by by applying a finite set of powers of two generators of an isometry group to a point in \mathbb{R}^3. This provides an interesting link to the theory of "objective structures" of James, which can be viewed essentially as the union of orbits of a discrete group of isometries on a finite set of points in \mathbb{R}^3. The distinction is that the generators used by Twarock do not generate a discrete group. There are a great many nondiscrete groups of isometries and the subfamily used by Twarock enjoys a certain uniformity property. As explained by Twarock, there are links between these ideas and the "method of projection" from higher dimensions used to construct quasicrystals. The possible implications of this circle of ideas is that potentially a large class of non-periodic (and non-objective) structures seen in Nature, including possibly quasicrystals, polymers, glasses, can be viewed as the action of a nondiscrete group of isometries on a set of simple structures.

I found the workshop extremely useful on several aspects. On the one hand, I was able to present my work in front of a very selected and high quality community, which is hard to gather together in the same room in a standard conference. On the other hand, I was able to have discussions that helped me move my research forward. Additionally, I established long conversations with another attendee which is likely to be the beginning of a collaboration. Thank you for the great organization and for making this type of workshop possible.

It has been a great meeting with a high impact on my current research.

I very much appreciated being part of the Mathematics and Mechanics in the Search for New Materials workshop, organised on the occasion of the 60th birthday of Dick James. I had the opportunity to refresh several of my long standing collaboations with people in this field, get first hand information on some new opportunities for joint research and provided some of my colleagues at home with potentially interesting new contacts. I also very much appreciated the beautiful surroundings of the centre.

Physics, University of Antwerp, Belgium

The workshop gave me a great opportunity to learn in-depth about the current development in various sub-areas of complexity theory. The workshop will likely inspire several projects in the next year or two. Conversations with Sasha Sherstov and Scott Aaronson inspired me to look for an information complexity attack route on the (notoriously hard) Arthur-Merlin communication complexity model. The talk and conversation with David Steurer encouraged me to start looking for another proof for the Parallel Repetition theorem. Overall, it's been a wonderful and important experience that will impact my group's work.

Computer Science, Princeton University, Department of Computer Science

I participated in the workshop on complexity which took place in July 2013. It was an amazing workshop - I got to hear about recent development in the various areas of complexity theory and to discuss potential research directions with many of the attendees. There is even a potential new research direction that emerged from our discussions; as well as many "old" hard problems which we discussed and brain-stormed about. For me, this is the third time I am in this workshop (previous times were in 2008 and 2010) and I have to admit that this is one of the best workshops in complexity theory that I know. This is because of the unique mixture of a beautiful and relaxing surroundings; an amazing host of participants at the workshop; great organization and selection of talks; and an environment which supports academic collaboration in as hassle-free mode as possible.

This workshop is always wonderful; it presents many of the most exciting recent works in complexity theory. I heard about new results and useful techniques; learned about work very related and relevant to something Scott Aaronson and I proved; and benefited from giving a talk about something still in the works.

The workshop was a very productive experience, both in terms of learning about new results in the area as well as informal interaction with existing and potential collaborators.

I had an excellent professional experience during the Computational Complexity workshop. In addition to the very interesting and informative slate of talks, I was able to re-connect with collaborators and push forward several research projects. Some of the discussions we had at BIRS have re-invigorated research projects and given us new approaches.

I learned a lot on various on going work as well as very recent achievements on the field, i.e., the computational complexity theory, that I have been working. When coming back, I have told several important topics discussed in the workshop, which may be very informative to researchers in our group. I am extremely happy to get some new results out of discussions with the participants of the workshop.

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology

My participation in the BIRS workshop contributed to my research in several ways: It helped communicate recent finding with the community. I have learnt of new problems and some of them are already on the way to being solved. I got a much better understanding of the main themes of current research.

For a person like me who is trying to choose his field of research for future, it was a great conference to start with. I learnt a lot, interacted with masters of the field and got inputs for my SSL(Sequence Specificity Landscape) program. After seeing everyone's interest in the field and towards my work, I am now excited to continue working on this project and improve my programs so that it can be helpful for analysis for other people too. I new about research of few people who presented, by this meeting I was able to clear my doubts by asking them. Also learnt about research of lot of other people in the area, which is equally exciting and challenging. This conference has filled in me the interest to work on research, specially in the area of DNA-Protein interaction.

Department of Biochemistry, University of Wisconsin

Thank you very much for hosting the workshop on Rules of protein-DNA recognition. The meeting was spectacular! Very high quality talks, all highly related to my research, and also very inspiring. Alexandre Morozov and Gary Stormo did a great job putting together such an excellent scientific program. It was great to have, in the same room, so many professors who have pioneered the computational models and the experimental techniques I am currently using in my research, and the discussion times allowed me to better understand the details of each model/method, as well as compare and contrast the various existing technologies. In addition, several collaborations were initiated during this workshop. Remo Rohs, Matt Slattery and myself are going to write a review on the topic. David Lukatsky and I have already exchanged data and results, and we are now talking about writing a paper together. Alex Morozov and I have started a new collaboration - we are now trying to use his thermodynamic models on some of the data I am generating in my lab, and we have already discussed some ideas for future projects. I expect that other discussions during the meeting will also turn into collaborations later on. So, in conclusion, the workshop has helped me a lot in my research, both in terms of immediate effects, as well as inspiration for future research directions. Thank you again for making this workshop possible!

Looking over my notes virtually all talks provided me with a new valuable nugget of information. However for my work directly, several talks had a significant impact: Phil Bradley & Carlos Comacho: Provided computational support for the idea that water plays a consistent, potentially (structurally) predictable role in forming protein-DNA interfaces. Phil's ideas that there are solvent 'rotamers' will greatly assist in efficient prediction of hydration schemes. Carlo's finding that differential solvation of a particular protein-DNA contact in different protein or DNA sequence contexts provides a potential (and likely correct) explanation for 'non-linear' effects of substitution mutations on protein-nucleic acid complex affinity. Tali Haran: Injected a note of function and reminded us that binding protein concentration and not just sequence, are important elements when considering functional binding site occupancy. Scot Wolfe: For illustrating his method for selecting not only preferred DNA sequence, but protein sequence outside of the interface region. Aseem Ansari: While not earth shattering, the sequence preference 'landscapes' will provide novices in the field with an easy to read way to identify interesting features of selected sequences. The practical outcomes via new methods to be employed and collaborations was almost as valuable as the ideas. Collaborations: Phil Bradley and I will begin a collaboration on large scale prediction of protein-DNA interactions in bacteriophage repressor proteins. This effort will have a significant impact on testing hypotheses related to how toxin-encoding bacteriophages have evolved to have a 'hair-trigger' induction mechanism-a feature that may lead to their increase virulence. We sent the first set of 'test' data to him today! New methods: Having failed at using purified chimeric transcription factors to identify cooperative changes in preferred binding site motifs, the information on bacterial one-hybrid obtained from Scot Wolfe's and Marcus Noyes' talks and informal interactions with them have emboldened us to try this route. We ordered the oligos and DNA yesterday. We hope that experiment will be complete by the next meeting!!

Department of Biological Sciences, University at Buffalo (SUNY)

This was an extremely productive meeting for me. It gave me a chance to see how my research projects might fit into the goals of the protein-nucleotide world. I met many people whose papers I had cited but had never crossed paths with before. I discussed potential collaborations with other participants, based on both published and unpublished work. Attending with a close colleague and collaborator, the meeting helped us put our upcoming paper into the context of the state of the field. It has also been very helpful in our thinking about future projects and an upcoming proposal.

The meeting was a great way to learn about new tools, their power, and their potential pitfalls. I will include what I've learned in my teaching next year. I also got a chance to network with several people I might collaborate with in the future, and to spend some focused time with a current collaborator from a different institution. Also, we really really really appreciated how helpful BIRS was when we were marooned in Banff. My extra time there was very productive.

This was a wonderful meeting. I like this kind of small meeting focused on specific topic rather than large conferences, especially in this perfect environment. In spite of the small meeting, there was a good mixture of presentations from different backgrounds. I listened to all the talks, and all of them were interesting and useful to my research. I was impressed by the progress of this field, especially new experimental methods and new tools to analyze them. This meeting helped me to expand the scope of protein-DNA recognition. I could meet many new people and the discussion was very stimulating. All the talks and discussions were inspiring and lead to new insight into the mechanism of protein-DNA recognition. This meeting also provide me a possibility to collaborate with some researchers.

Kyushu Institute of Technology, Kyushu Institute of Technology

The BIRS workshop on protein-DNA interactions was really superb. It brought together people working on a common topic, protein-DNA interactions, with a variety of experimental and computational approaches. Although I had previously read papers by most of the participants I had only met about half of them. The talks generated several new ideas that we will test and possibly some new collaborations. It definitely will have an impact on our research directions.

Department of Genetics, Washington University in St. Louis School of Medicine

The range of topics related to protein-DNA recognition that was the highlight of the meeting. The opportunity to hear both experimental and computational approaches related to protein-DNA recognition provided the opportunity to expand my perception of the key questions that remained in the field, and the suite of approaches that are being used to achieve greater understanding of the biological questions that still remain. The meeting also provided a great opportunity to strengthen interactions between my laboratory and the Stormo and Noyes laboratory. In addition, new potential collaborations were defined with the Hughes lab on protein DNA-binding specificity and the Bondos lab on artificial homeodomain recognition. Opportunities to discuss science over meals were particularly valuable with both theoretical and experimental approaches being weighed for particular questions. Alex Morozov and Carlos Camacho provided very valuable critiques of an idea that my lab will pursue on homeodomain evolution that will affect the planned direction of these studies. This was by far the most valuable meeting in this field that I have attended.

Program in Gene Function and Expression, UMass Medical School

The program was diverse and at the highest level of the field. I have happily reconnected with some old friends and made new ones, thanks to this conference. We started some new collaborations. Thank you!

This is my best workshop since many many years. My participation impact and help strongly my research: - many answers given by specialists, and such answers are not written on books. - A new possible collaboration with a leader in the field starts! Thank a you a lot for this marvelous center in such beautiful mountains. Thank you Brenda, Joseph and all the BIRS organization.

The main value of BIRS was the possibility for the informal discussions over the course of the week. I took advantage of the opportunity to trade ideas with people who I normally would never see in any other circumstance.

It definitely impact my research in a very positive way, giving a more general vision of the current achievements, and it allowed me to directly talk with people involved in research projects very close to mine. It also allowed me to talk directly with my 3 actual coworkers, all of them participating to the workshop.

Mathematics, Universita di Bologna

I have attended 3 other BIRS meetings, and this was easily among the best. The discussion was unusually lively, and it was very clear that the audience was engaged with essentially every speaker (often at meetings with disparate backgrounds some subset of talks simply get tuned out, and this did not happen here). I had that one crystalline idea, that came out of a question session at the meeting, that will very likely end up as a theoretical paper, and for me this is an excellent criterion to judge whether a meeting was a success. Systems Biology is a challenging area, with lots of different ideas about the direction it should go, but the organizers did an excellent job in identifying participants that share a common interest in rigorous quantitative methods, and that was sufficient glue to hold it all together.

Molecular Biology and Genetics, Cornell University

My participation in the workshop has given me the opportunity to meet many new people that work in the same field of study, and it was an excellent test bed to find out if certain ideas and/or plans are worth further investigation. The informal discussions over lunch and dinner were a great source of new knowledge and various new ideas. Support from the Banff Centre was flawless, the fitness centre and swimming pool a luxury I didn't anticipate, and the Maclab bistro a nice place for a drink.

Centre for Genomic Regulation and Universitat UPF Barcelona

It was a fantastic meeting, a great mix of people I already know, respect and always want to hear from, together with others whose work was new and interesting to me. Talks and informal breakout discussions prompted a big "ah-hah" insight for me, clarifying a problem I had long been wrestling with, and which has now finally come together. This insight will soon go into a grant proposal, a paper, and maybe a whole significant research direction for me, one which might include a collaboration with somebody I met for the first time at this meeting.

The BIRS workshop I attended was a critical step in bringing together mathematically minded people from Evolutionary Biology and Systems Biology. If the mathematical methods in these fields are unified, I believe we will look back at this workshop as a key step in that development.

University of Toronto

Great workshop, which has probably resulted in one collaboration for me.

Scientifically the workshop was one of the most useful and impressive that I have attended in my career. The selection of speakers was outstanding, and what was particularly useful was that I was brought into contact with people from related fields that I would not have otherwise come into contact with. This has had important impacts in the way I am thinking about the problems I am working on. I also think that the setting, in a beautiful place where it is not too easy for participants to leave the venue, together with the communal meals at a single location, highly contributes to meaningful interactions between the participants. I hope that it will be possible to organize follow-up meetings of this kind, because they are highly effective.

Expanded my horizons, certainly. New contacts made. A few new research ideas and possible directions.

The work shop was great. The size of the meeting was just right enough to be able to meet everyone. I learned a lot and had a very good time. The center is so well organized, it's amazing.

This was an extremely good event. The programme was both very stimulating and comprehensive. All the participants clearly took it seriously as the papers and contributions were all very well done. Personally, I learned a lot and left with a considerable amount of new knowledge and much food for thought, which will have a long-term influence on my own work and that of some of my collaborators. It was also a great pleasure and a privilege to be invited and to be able to spend a week at BIRS. This is a superb centre; a tribute to those who created, developed and funded it. And of course to those who run it today: we were made very welcome, the friendly and supportive atmosphere created by the BIRS staff undoubtedly enhanced the workshop. It was also good to be reunited with some well-known skew-ellipticals, other folk that I’ve met before and to meet new people. Not for the first time, I was reminded that statisticians are a great group: invariably smart and always fun to be with.

The participation to the workshop on "Non-Gaussian Multivariate Statistical Models and their Applications" was a wonderful experience of which I shall keep a most pleasant memory in the years ahead. The BIRS organisation and facilities are outstanding, in an exceptionally beautiful location, and it was clear since the beginning of the workshop that the days ahead were going to be most stimulating. Indeed, in the following days, the presentations and the discussions, both in the formal and in the informal occasions, have been up to that initial perception. The workshop has offered the opportunity deepen interaction with people that I already new, but even more importantly I had the chance to meet people of whom previously I had only known the publications. Getting together with them and talking informally in a comfortable atmosphere has offered the possibility of perceiving new perspectives. All of this is offering to me a wider perspective of the theme were I am involved as well as a chance of new collaborations. I believe that the organizers have put together an excellent list of names, blending together contributions from different but related streams of the literature. This will contribute to a step forward of the discipline.

Scienze Statistiche, Università di Padova

The workshop went off very well, with lots of interesting presentations and discussions about the past, present and the future with regard to research in the focus of the workshop. Everyone enjoyed the event, the location and the facility immensely. A small group of us also discussed the possibility of putting forward a proposal for another workshop on the theme of "Stochastic Orders and Their Applications" and with special focus on reliability. I am meeting with two of them in a few weeks time in South Africa in a major reliability conference when we may finalize the details so that we can put forward a proposal. Overall, the event was a grand success and thanks for providing an opportunity for us to organize this workshop on Non-Gaussian Multivariate Statistical Models and Their Applications.

Many people participating in the workshop have a high research level. It was great to have the opportunity of hearing them in live. I have had the opportunity of knowing them and also of meeting another people that otherwise I wouldn't know. In my case, this unexpected contacts have been the most promising, in the sense that I have been discussing some ideas with them that hopefully will yield new future research projects. In summary: I have learnt many new things and I have been discussing about new research projects with professors that I did not know before.

It was a great opportunity for exchange with colleagues. The level of the talks and the discussion was superb. I have particularly appreciated the fact that in this meeting two different groups of researchers were put together to discuss a common problem. I have learned different perspectives for my own research.

MEMOTEF, University La Sapienza of Rome

This was a wonderful workshop in an inspiring location. For me it was an opportunity to meet in the flesh some figures in the area whose work I have been reading for a number of years. I now have a series of ideas to follow up and a number of potential collaborators. I feel certain this workshop experience will lead to new research outputs and I return home reinvigorated.

Actuarial Mathematics and Statistics, Heriot-Watt University

The workshop was quite stimulating. I also got the chance to work with two of my coauthors and we made substantial progress on our joint project by solving a tricky convergence result about empirical processes with pseudo observations. Otherwise, I was happy to meet new colleagues and spend a week in such a charming location.

Mathematics and Statistics, McGill University

It was a wonderful opportunity that top researchers in both skew-symmetric distribution and copula gather and discuss different aspects. Meeting top researchers in both fields is a treasure in my research life. I have learned a lot on both fields. Discussions stimulate my new research directions.

The meeting at BIRS last week was very well organised by Mark, Alan, Peter and Henri, as well as being academically really interesting and stimulating. I met up with some colleagues, made a number of new contacts and outlined some potential new collaborations. If any of these blossom into substantive pieces of work I will ensure that BIRS is both informed and acknowledged. In the meantime, very many thanks for the hospitality and facilities at the Banff Centre; altogether this made for a great week.

The BIRS workshop last week (Impact of Climate Change on Biological Invasions and Population Distributions) was excellent, and has already had a strong positive impact on my research program. During the workshop, as a result of ideas arising from talks I heard and discussions with colleagues, I have come up with a new set of approaches for one of my research questions, fresh insights into the work I am currently doing, and an associated research program for my upcoming PhD student, to arrive in September. I have also been invited to visit one of the workshop participants in Oxford next summer, and have set up a new research collaboration with two other participants. The latter will hopefully result in a publication.

This workshop is great. I definitely learned a lot from high-quality talks and excellent participants.

Mathematical and Statistical Sciences, University of Alberta

The workshop organized by Mark Lewis et al is wonderful: Worldwide active leading researchers get together to discuss the topics, I've learned a lot from many of the participants and their talks and discussion. Guess that others at the international level also got to know what I have been doing. It's great! I am thinking of organizing some workshop in the coming competition.

The workshop was really useful. A special thanks to BIRS for providing such a nice, warm and, friendly environment.

That was an amazing conference. It was specially useful for graduate students to see what type of research is being done in other universities close to home.

The meeting was very revealing, and gave me quite a number of new directions to think about. Also, I found all talks interesting, and almost all very well presented -- which is to say that the organisers made a very good selection ! The visit was thus extremely fruitful

First, the workshop gave me a chance to catch up with some of the latest interesting developments in the field. And second, it gave me a chance to talk closely with a couple of colleagues I have been wanting to bounce some ideas off of. I am optimistic that at least one of those discussions (one with Rafe Jones, another with Par Kurlberg) may lead to further developments. Third, I was newly inspired by some of the questions about expected cycle lengths and orbit structures in generic rational functions over finite fields. I have thought about some of these questions before, but the workshop gave me new ideas and insights, not to mention renewed enthusiasm for some of these questions.

Thank you for a great scientific experience and a very well organized and pleasant stay.

This conference was quite unique in my experience so far: The topic is perhaps a relatively new (emerging?) topic, and not yet crystallized: most people felt as if they approached the topic "from the side" i.e. that they were approaching the topic from "their" field. This meant that at this conference you found quite a diversity of backgrounds, but all of them interested in the topic at hand. I found this to be very stimulating: the diversity of type of questions, approaches, and knowledge was as refreshing as freshly pressed cool orange juice!

It was wonderful. I have never come back from a conference feeling so excited about opportunities for new research directions. I am very grateful to the organizers. The environment at BIRS also made it a very pleasant experience.

The week I stayed at Birs for this workshop was excellent. The organizers did a very good job, inviting researchers who are active in the wide area of dynamical systems on finite fields (and beyond). The talks were very stimulating and "inspiring creativity", as Banff Centre aims to be. Nevertheless, the accommodation, the weather and the landscape were wonderful and all these elements made the workshop even more successful.

This area of research is new, interdisciplinary, and rapidly evolving, and this timely workshop provided a unique overview of it, thanks to the skills and complementary interests of the organizers. It was BIRS at its best: plenty of interactions, high standard of presentations, and miraculous weather.

I met with coauthors and finished a paper. I learned a few new things but it is too early to tell their impact on my research. I met some people who might be interesting job candidates in the future. I really enjoyed the meeting. Nice talks, nice people, nice weather.

As a senior researcher, I know most scientists (except for newcomers) at most conferences that I attend. This workshop was different. The organizers have put together an interesting group of people working on related problems but from very different directions, many of whom I had not met before. I saw many interesting problems and perspectives. In fact, I will study some of the problems that were posed at the workshop. Several colleagues commented to me along the same lines. Great applause to the organizers for putting together an unusual and highly successful list of participants.

Computer Security, B-IT, University of Bonn, Germany

The workshop brought together researchers from two different areas, finite fields and dynamical systems. I expect many fruitful scientific cooperations between people coming from these areas. Personally, I got several new ideas for future research and met new people who may become co-authors soon. An invitation to esteemed research institutes as Banff, Oberwolfach, ... is always an honor and a plus in any CV. Moreover, I had the opportunity to meet co-authors to discuss running projects and organizing workshops.

RICAM, Austrian Academy of Sciences

This was a great workshop in a fantastic place. Congratulations to Tucker and George for putting together a great program. The facilities and staff are first-rate at BIRS so congratulations to you as well. I know many participants hope to return for another workshop in the near future.

it was a great experience. the stuff was extremely organized and professional. the facility is first class, and the food was great! thanks you for your service, we had a great time.

A main goal of this workshop was to bring together theoretical chemists and mathematicians who are interested in molecular quantum dynamics to exchange information. It was highly successful in doing this. Chemists learned of recent mathematical results from mathematicians and mathematicians learned what problems are important to chemists, and what the state of the art in chemistry is. Several participants have sent me e-mails commenting on how successful this workshop was in bringing the two groups together. I presented a talk on a simple mathematical model for molecular Rayleigh and Raman scattering. Chemist Todd Martinez (one of the chemistry participants) has worked on this subject from a chemistry perspective, and he had several questions for me that have caused me to do further analysis of the problem. I have also had subsequent e-mail communication with William Miller that will change my future work on this subject. I have also met several times with Edward Valeev (another chemistry participant) since the workshop. He and I have discussed what we have learned from Todd Martinez and William Miller, and we have discussed the further analysis and future directions to be pursued. He and I have also discussed other topics we learned about during the workshop. One of Ed's comments a few days ago was, "It's fun to discover connections between ideas. It's amazing how much we can learn from one another." The venue was spectacular, and the staff support was the best I've experienced in a very long time. (I was an organizer.) Everything went very smoothly. Thank you!

The joint meeting of scientist working mathematics and theoretical chemistry inspired very interesting discussions quite different from the more routine communication in "conventional" workshops or conferences. Everything was perfectly organized!

The workshop was very good. It allowed me to present to people who work in related areas to the topic of my presentation our work that perhaps went unnoticed previously. Advantages and disadvantages of different methods could be discussed with their developers. I cannot say new project/collaborations originated from the workshop, but possibilities thereof were discussed and it is possible there will be new work resulting from the workshop.

The SNAP Foundation is a non-profit organization whose mandate is to encourage the development of mathematics learning resources at the classroom level with very little retraining of the teaching staff, with very flexible budgets, and by utilizing the energy and natural curiosity of the students themselves. The main theme of the BIRS workshop was, “What is a SNAP math fair and how to organize a math fair in your classroom”. The speakers mostly consisted of teachers/educators who shared their math fair experiences and success stories. The first SNAP type math fair was designed in Edmonton by Mike Dumanski and Andy Liu in 1997-1998. Since then, a large number of schools in Alberta and beyond have adapted the SNAP math fair to their needs. The SNAP program has been spread through similar workshops and conferences, and mainly by teachers themselves. SNAP received its initial funding from the Canadian Mathematical Society and from private donations. PIMS, the Pacific Institute for the Mathematical Sciences, has been a long time financial supporter of our math fairs. BIRS, the Banff International Research Station, has provided funding for the BIRS math fair workshops that have been held in Banff on a regular basis. Currently, our major supporter is Thinkfun - a company that develops a variety of excellent puzzles. This year marked the tenth annual Ted Lewis SNAP Math Fair Workshop at BIRS. Some of the feedback from elementary teachers is given below: “I had a terrific time with the group! Thanks for sharing all of the ideas and puzzles!” “Thank you so much for the invitation to the SNAP Math Fair Conference! I am absolutely thrilled with the possibilities I have to bring math alive in my classroom and school. I am so excited to spread the information, websites and puzzles that I was able to gather at the conference. I greatly enjoyed hearing the various perspectives on math fairs and can't wait to plan one of my own. Please keep me on your mailing list and inform me of other SNAP activities that I could participate in.“ “Thank you for organizing this event. I know that my kids love playing games, so any new ones are always welcomed in my room. It was fun as always and it hurt my brain just a bit.” Thank you BIRS for providing a location for another successful workshop. We are extremely grateful for what you do to help SNAP math fairs grow. Sincerely, The SNAP Foundation

The meeting gave me the opportunity of contact with some specialists in C*-algebras I wouldn't have meet in other circumstances. And also helped me to reconsider some of the lines of my current research. I expect that it will produce positive influence in my present work. And definitely, the meeting will produce a very important impact in this topic of research.

Mathematics, University of Cadiz

The workshop was very interesting. It showed the most recent developments in this field of arithmetic groups. The subject has a long tradition, but new insights, questions and ideas, as well as young people came into the field and these made this workshop very successful. Let me mention in particular the work on expanders and on growth of representation dimensions leading to new Zeta functions. There were also mini courses on recent subjects, where one had a chance to not only see the results but also to get a feeling for the methods involved in how to approach the problems and how to obtain the results. Three of those come to my mind, one on the recent solution of an old problem, the so called rank theorem, one on pseudoreductive groups, which solves some hitherto technical problems around non-separability and positive characteristic and one on Kac-Moody groups, a field that gives for mathematics new and interesting examples of groups and also has applications in physics. I think this was a very successful workshop. It also gave young people the opportunity to present their work. It fine tuned my opinion about two of the participants. It also gave very young colleagues the chance to see the forefront of current research. The workshop also gave me the opportunity to meet colleagues I had known for a long time, intensify my scientific contacts with them, but also to get to know more closely younger people who are new to the field.

Indeed the workshop was useful and stimulating. I would also like to record here my appreciation of the excellent arrangements made by BIRS for the stay of the participants: that contributed no little for the success of the workshop.

I enjoyed the conference very much. It brought together several disciplines within mathematics, which was great. I wouldn't want every conference to be this way, but here are two big pluses this time: First, several of the expository talks were really quite good, and broadened my knowledge to greater familiarity with these other disciplines. Second, and most important, two conversations I had in particular with members of another discipline provided a new, useful view on a tangentially related current research project of mine.

Last week's workshop at BIRS was an outstanding event for me and for my research. I took advantage of many extremely interesting talks, and of having the possibility to meet and discuss with some of the main world experts on mapping class groups. These 5-day workshops, with few but very good researchers toghether at an extraordinary environment, provide the perfect conditions for discussions, interactions and development of research projects. This was my case indeed. Thank you for organizing this kind of meetings, in particular this one and the other two I attended previously (on braid groups, some years ago).

My fourth visit to BIRS was, like all those visits, enjoyable and interesting. The somewhat unusual conjunction of topics in this meeting stimulated me to think about connections between mapping class groups and Floer-thoeretic questions in symplectic topology (the latter topic is what my research is about). I asked the mapping class group experts a number of directed questions about properties of mapping class groups which might potentially apply also to symplectic mapping class groups in higher dimensions (the basic connection being through the notion of a Dehn twist). Based on their answers, I came away with a number of definite and novel problems in symplectic geometry (some ambitious, some less so) which I or my students might well work on in the future. I'd emphasize that it was the topic of the workshop and the presence of experts that stimulated this line of thought.

The workshop was extremely interesting with top speakers in the area and very interesting talks. There was also time for very fruitful interactions with the participants.

This is clearly a well organized workshop with a good selection of timely and interesting talks. I benefited personally from attending this workshop in many ways. During the workshop, I had good discussions and consultations with some of the world's leading experts in mean field games and other mean filed approaches for social dynamics. For sure my future research directions will be influence by this workshop. In addition, the organizers invited well qualified junior researchers to the workshop. This is very helpful for "talent hunt".

I had a great time at Banff and left with several new ideas and a lot of inspiration. One new project has to do with finding ways of using our bordered monopole Floer invariants to compute relative invariants of 4-manifolds with boundary. This was inspired by David Gay's talk on his work with Kirby on trisecting 4-manifolds.

Mathematics, Boston College

Every time I come to BIRS I come away with lots of new ideas. This time, though, I had some new ideas that haven't been exposed much to the public and I really appreciated the opportunity to run those ideas by my colleagues in detail. I established at least one new collaboration partnership, with Joan Licata.

As was the case of each of the prior 3 workshops on "Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4", the meeting in March of 2013 was truly incredible. I found that the lectures at this workshop were among the best and most relevant to my research that I have seen at a conference in recent memory. I had several inspiring conversations over meals and on mountain hikes, and came away from the workshop full of ideas and mathematically invigorated. This has been my experience with each of the meetings of this biennial workshop, and I very much hope that the workshop will continue in 2015. I think that of all the conferences or workshops of my mathematical career, these meetings have been the most influential to my research.

This was an excellent meeting, with a good mix of mathematical subjects and participants. For me, it was particularly useful because I met three collaborators from three separate projects, and made progress with each one. One of those collaborators was someone I rarely get to see face-to-face, so it was particularly valuable for us to be able to talk between the lectures and in the evenings.

Mathematics, Brandeis University

The week at BIRS (off teaching duties, off kids, with inspiring people around) was perfect. I got a lot of work done, new ideas coming up, a paper finished. Many people seemed interested in my work. It was truly wonderful. It's hard to say if the workshop affected my students' job prospects, but contacts and staying in touch and publicizing our work surely has a long term affect on this.

Mathematics, Tel Aviv University

This was not my first participation to a 5-days BIRS workshop; it was maybe my fourth visit to Banff and BIRS, and every time I come to this place I love it more! During this particular meeting I could present a part of my recent research, and it was a good occasion to exchange opinions, ideas and impressions with other participants who are working on the same, or on similar, topics, in particular Vitali Milman, Liran Rotem, Artem Zvavitch and Dima Ryabogin. This exchange will influence for sure my future directions of research. Moreover I had the opportunity to work with Monika Ludwig, a participant from Vienna, on the research subject that I am liking most in this period, i.e. classification of valuations on function spaces. We had several fruitful discussions which helped us to enter a bit more in this topic, which is still almost unexplored. BIRS represents for me a place where I can devote myself entirely (or almost entirely) to do research, forgetting the rest of the world for one week!

Mathematics, University of Florence

This stay at BIRS had important impact on my current research, since after the talk a colleague mentioned some techniques that I was not aware of. Additionally this led into new collaboration.

Institute of Analysis, Johannes Kepler University Linz

The perfectly organized workshop at BIRS stimulated my interest in some new and important questions which were presented in the talks. I am quite sure that this will lead to new publications on these important problems on the borderline between convex geometry and Banach space theory.

There were three talks that I liked very much. This is much more than I usually experience in a one week conference. These were the talks by Monika Ludwig, Dima Ryabogin and Shiri Artstein (she gave two talks the second on Friday after I left. I'm talking about: "Viterbo's conjecture implies Mahler" which included a very nice introduction to symplectic geometry). I also learned about a result of Prochno and Schutt in a talk by Prochno (I should have known about it independently of the conference but somehow it escaped me until now). I managed to simplify and generalized their main result and am writing a short note about it.

For the past two meetings which I attended at BIRS, I met people from my field who I almost never see elsewhere, hence the chance to talk on specific problems, still open, in my area. At this particular meeting, I also appreciated the variety of talks many of which reported on recent progress. Overall, the meeting was very beneficial for my research in what concerns both the update in the field and the professional contacts.

Really appreciate that BIRS provides a wonderful research environment. It was always my pleasure to be there for great research workshops. Thanks for your great job.

It is so nice for geometers and analysts gathering and exchanging ideas. The organizers did a great job. The program and the speakers are carefully selected and arranged in a professional way.

The application of Iwasawa workshop was very useful and stimulating for me. It had so many interesting talks which gave insights into various different areas of Iwasawa theory, which is my area of research and also gave a clear idea of the directions where the research is moving and also what are the new topics that are coming up in this area of arithmetic geometry. It will have a positive impact on my future research work. (I am a postdoc myself, so in my case the question of impact of the workshop on hiring is not applicable.) Thanking you once again for giving me this excellent opportunity to attend the workshop.

My participation in the BIRS workshop had a great impact my current research, through which I talked to the experts in the field and had very insightful conversations. Some of the talks were directly related to my research problem, but I found the discussions that I had over coffee breaks and dinner were more helpful for my research problem. The talks given in the workshop were more helpful to me in the direction of expanding my understanding how Iwasawa algebras are used in other fields, and I think the latter point is as important as the former one regarding my own research problem.

I found the workshop extremely interesting and productive. During the week I was there I completed one research paper (joint with two other participants), made substantial progress in another existing project, and began two more completely afresh, neither of which would have happened if I had not attended the workshop. Altogether this week was one of the best mathematical conferences I have attended in my career so far.

Mathematics Institute, Warwick University

There have been quite a lot of very interesting talks. In fact, I recommended some of the videos to colleagues (not only the video of my talk). Aside from the talks, I had the opportunity to discuss a problem (which arose in my current research) with some specialists in the field. It seems that this was very helpful and will eventually lead to a solution of this issue.

The workshop was stimulating and encouraging. I received useful feedback on a project I'm considering, and questions about applications of my work to other areas of interest. Some colleagues even raised prospects of visiting positions in the future.

Department of Mathematics and Statistics, Boston University

We had a very good conference last week in Banff and many of the youngsters from different parts of the world, who were first time visitors to Banff, deeply appreciated both the mathematics and the place!

BIRS and the Banff Center together with its calm and charming environment among the beautiful mountains provided an ideal atmosphere to present, communicate and over all discuss mathematics in all its depth. In particular young mathematicians had the opportunity to profit from this intense workshop which also offered the opportunity to report on their PhD thesis.

BIRS is a wonderful place to work and to collaborate. Yes, the workshop will have an impact on my research, yes I learned many new results at the workshop, yes I made new contacts that I wouldn't have had otherwise, yes it influence an hiring decision I am involved in. Thank you for providing such a wonderful place.

mathematiques, Universit'e Paris 7. Institut de mathematiques de Jussieu.

This was an outstanding workshop which triggered a lot of discussions and exchanges. My main technical discussions have been with D. Gamarnik (MIT) on local algorithms, Augustin Chaintreau (Columbia) on random graphs, and Andrea Montanari (Stanford) on point processes.

My time at BIRS was indeed very stimulating. In addition to many interesting discussions, motivated by some of the talks in the workshop I have formulated a couple research problems, which I will begin working on soon. Thanks for providing such nice support and venue!

The workshop was a fantastic time to bring together people working on high dimensional inference and on the analysis of social network dynamics. I think we have rarely a chance to all interact and this was a perfect setting and size to get the most of this interaction. On my side, one of the person I met there who is in the same area will probably be joining my reading group and I hope that this will initiate a great collaboration. I also started chatting with another person about a possible follow up of her work. I think Banff, the excellent environment and the quality of the program made us all aware that they are potential research benefits that we had missed in our respective communities due to rush schedules. I look forward to attending more events organized at BIRS.

The workshop was very good and we had numerous interesting discussions. The posting of the talks online is great and a valuable asset for my students and the community more generally.

This workshop definitely brought me fresh insight and new contacts.

I very much enjoyed visiting BIRS, and I found the workshop very productive, as a significant fraction of it focused on topics I am currently exploring. The group of participants was well chosen, with closely overlapping research interests and representing the leading research in the field. I am looking forward to coming back to BIRS at some point in the future.

BIRS was a superb venue for the workshop. A beautiful and inspirational setting to discuss the cutting edge in our field.

Physics, Imperial College London

This was a wonderful workshop. This workshop stimulated at least two new projects and possibly one new collaboration. Time will tell if those projects bear fruit.

Physics, University of Victoria

I did enjoy the meeting and the facilities. I would like to thank you for this. I am glad you have such a nice center at the service of science.

It was one of the best workshops I ever had. We had meals & accommodations together so that we were able to discuss all day long. So, this was more like a summer school, but much fancier with great facilities and excellent staffs.

My visit at Banff has been a great opportunity to enjoy both the excellent scientific program and the outstanding organization. This was the second time I was invited (the first was in the framework of a meeting on Ricci flows) but the first time to come. It was a fantastic experience, where I realized the role played by art at the Banff Center. I was really delighted. I hope to have again the opportunity to visit the Center.

I appreciate the activity at the BIRS very much. It helped me a lot by hearing the response to my talk, which clarified a few points which I did not thought about before I come to the BIRS.

physics, Hanyang University

The conference was great. The program consisted of a good mix of leading researchers, many of whom are academically young and very active, several most relevant experimenters, such as Armitage, Hsieh, Drew and Hassan, and a couple of senior leaders in the field who gave the meeting great dignity. Overall the organization, quality of talks, and supportive environment made it a pleasurable experience which begs to be repeated.

Physics, Technion

The workshop was great and so were the facilities. Thank you and the staff. BIRS is a great place for doing science.

I'd like to join you in commending the fantastic organizational efforts of Professors Goldman, Peters, Sottile, including your amazing staff and facilities . The workshop was very productive, as it brought together and provided me the rare opportunity to interface with my peers from all over the world, and also to renew some very old friendships. Thank you sincerely, for all that BIRS is doing to further research in the mathematical sciences. These meetings are invaluable!

My participation in the BIRS workshop did impact my current research. The workshop participants included a very interesting mixture of theoretical algebraic geometers and applied geometric modelers. As a result, I obtained very positive feedback on my talk at the conference including several important questions that I plan to address in the future. I am trained originally as an algebraic geometer so the possibility to interact with many people in the applied sciences was also very fruitful. I was able to understand better the problems as they arise in applications. I also met several new contacts that I would not have had otherwise. The location of the institute is just amazing. It really inspires you to work harder. Being surrounded by nature fills the spirit with joy and energy to engage in new and ambitious projects.

It provides a broader perspective to the field and gave me an updated view of where things stand in algebraic geometry.

Computer Science, University of North Carolina

This was a great workshop at a great place. Probably, one or two new collaborations will result from that meeting.

Mathematics, TU Darmstadt

One very attractive characteristic of this workshop was that it aimed from the very beginning to being inclusive - i.e.to include researchers who were "users" of the algebraic-geometric techniques and results, or who faced specific problems motivated by concrete (practical or mathematical) questions, alongside with "specialists" in the pure, mathematical territory. So it felt easy and natural to ask questions. I learn a lot, sometimes from informal discussions at dinner or during coffee breaks with the participants. One comment from a participant led to a connection I was not aware of, another gave a natural motivation for why the study of certain objects is so important, while the "applied" speakers pointed out important research problems from other fields that rely on algebraic geometry, or that pose new questions of this nature. It has been a fascinating week! I came back with a load of new ideas and contacts with people whom I would be able to consult with, for that direction of my own research that needs more algebraic-geometric insights.

Computer Science, Smith College

The workshop was very helpful. It was new disciplinary group of people for me - I am a chemical engineer who works on developing systems that mimic biological pores, and I met many biologists and physicists that study the structure and operation of the pore itself. Learning about the mechanistic insights was very helpful and inspiring, I came back with new ideas. I also met with many scientists, some of which I am interacting with on potential collaborations. Overall, it was a great experience and very productive.

Department of Chemical and Biological Engineering, Tufts University

This workshop was characterized by exceptionally high level of scientific interactions and discussions. There were several important suggestions by some of the participants that I am going to incorporate in my research on nuclear pores. I have also started several new collaborations in the areas of polymer-grafted membranes, laser-induced florescence studies of DNA translocation through nanopores and single molecule imaging of chromatin dynamics.

Physics, Bar-Ilan University

The participation in the BIRS workshop impact on current research; no new results were obtained during the workshop, bu many new ideas! Possibly new collaborations.

This was an absolutely great meeting! I enjoyed every minute of it, and I have heard similar comments from other participants too. Not only that I learned a lot from it, but I also started to work on two new problems, one with Cristina Stoica and Holger Dullin, and the other with Ernesto Pérez-Chavela. While with Ernesto and Cristina I worked in the past, Holger is a new collaborator. It is unlikely that these opportunities would have occurred under other circumstances than this meeting. I am therefore very pleased to have been there. The atmosphere for top research was outstanding. Thank you for leading BIRS and making it one of the top research places in mathematics in the entire world.

The workshop was amazingly pleasant and useful. The organization in the BIRS is extremely good and allowed us to focus completely on scientific matters, in a very friendly way. Lectures and discussions were fruitful in bringing and sharing ideas. Personally, I believe I got new ideas for starting at least two new research projects. On the most materialistic level, everybody was impressed by the organization and helpfulness of the BIRS staff, by the quality of meals, by the landscape, by the wifi in particular.

It was a great week at BIRS. I worked up to now on subjects peripherical to the N-body problem. Now I am more or less up to date concerning the state of the art. This will be helpful for supervising one of my PhD students. On the other hand, a colleague and I discussed at BIRS and already started a new research project. Thanks!

Thank you very much for providing excellent opportunity and conditions to the workshop on Celestial Mechanics which was hold last week at BIRS. It is an excellent conference with many interesting talks, and is an excellent opportunity for experts to communicate with each other. It is my great pleasure to thank you and all of your staff members in BIRS for their excellent works.

I got more ideas in the 4 days I spent at this 5 day workshop than I do in a typical 4 months period at my home institution. I had numerous conversations, initiated at least one, and likely two collaborations, and am considering organizing a similar workshop in several years. The structure of having two afternoons free, with evening talks was inspired.

Mathematics, University of California, Santa Cruz

It is a pleasure for me to confirm that I found the conference very interesting and stimulating. From discussions with colleagues I had a new occasion of collaboration that I hope will be fruitful.

This is a wonderful and effective workshop in terms of new collaborations and new perspectives. Two new research projects will start and a new result is discovered. By discussing with some best experts in the field, some new questions are raised and some unexpected inputs are given. This is just an intensive five-day workshop with many exciting topics. In addition, the Banff center itself is an amazing place with lots of unique events. In the free afternoon on January 16, it gave me a chance to attend some dance and music events which are so great. It is a "short" afternoon I never forget.

Department of Mathematics and Computer Science, Virginia State University

I'm very lucky to be able to attend this workshop "New Perspectives on the $N$-body Problem". During the meeting, the other professors' talks gave me a lot of inspiration. Some methods I have learned from the meeting may be applied to my own research work. Moreover, inspired by other teachers, I can study some new and interesting problems. At the same time, I am very lucky to get personal guidance from many famous professors, which is beneficial to me for all my life. In particular, I would like to thank one of the organizers of the workshop Susanna Terracini, who gave me the chance to learn from many famous professors face to face. I also want to thank the Banff Center to provide the accommodation.

BIRS provided a perfect surrounding for an intense meeting with a not-too-large, not-too-small number of scientists from around the world. The conference room is superb: the rounded rows of comfortable seats enable a perfect view to the screen and the speaker and encourages discussions since people in the audience can see each other! All technical facilities, like WIFI access, projector, recording devices are more than up-to-date and the staff is incredibly helpful and well-organized. Whenever I have the chance to take part (or even co-organizes a meeting?) in an event at BIRS, I'll be there again!

Dept. of Experimental Physics, Saarland University

I had the opportunity to interact with international researchers who have worked on similar research problems. I enjoyed the discussions that provided me with new avenues to pursue in my research program. I am a junior faculty member who will soon need outside letters of support for my tenure file. This meeting provided me with the opportunity to present my research findings and interact with the leading experts in the field I work in. I know the impact of this meeting will be significant in my academic career.

I had a brilliant time at BIRS and would like to extend my thanks to all those involved with the organization of the week. The talks were interesting and the extended discussion periods after each two talks I felt were a particularly good idea, given how well the audience participated. Whilst not directly impacting on my research now, there were a number of useful conversations I had, which have given me possible ideas for future research, and the chance to make face-to-face contact with many people of whom I have read journal articles and reviews was excellent.

Chemical Engineering, Imperial College London

The workshop was exactly the right setting to present some interesting results we had in the near past, as I met exactly a group of people that struggles with some issues that we can hopefully help to solve with our approach. The intense discussions that followed my talk told me that we are on the right track and should continue working in this direction.

I've been to meetings at BIRS before, but somehow this one was more intense and more focused than before. Pretty much all of the participants got fully involved in all aspects of the workshop (including the discussion sessions) and the week just flew by in a rush of scientific discussions and presentations. The talks are all very good and even the one which wasn't really quite aligned to the workshop theme (not the organisers' fault as the speaker changed topic at the last minute) was interesting. The facilities in BIRS and the Banff Centre were, as always, excellent and the food outstanding. There was some confusion about streaming and/or recording or the presentations, but this is a very minor point. The meeting was one of the best I've ever attended and has already lead to new scientific contacts (and, just as important, renewing of old ones) which will, I am sure, lead to new (and renewed) scientific collaborations in the future.

Department of Mathematics and Statistics, University of Strathclyde

This was a very productive meeting for me. The discussions relating to my general programme of research were very useful in the sense that it has brought into focus some key questions. Also, the very high level of participants meant that I learnt very new ideas from the real experts. Remarkably one breakfast conversation (over an hour) was one of the best explanations of mirror symmetry I have ever heard. In summary, it was truly excellent.

Great workshop! fantastic place.

We had very stimulating discussions with Michelle Bucher and Koji Fujiwara.

I hope that new results will come out of the conference. But this is too early to be confirmed. Anyway I got a lot of new insights and ideas.

Mathematisches Institut, University at Bonn

I heard talks, learned new things about orderability of groups (from Dave Morris), gave a talk myself, and received some feedback on my questions concerning the Atiyah problem. Thanks a lot! The environment is indeed very inspirational, great place.

The whole environment of the Banff Centre and the BIRS facility was extremely conducive to making progress with the goals of the workshop. The manager of the BIRS faclility was very helpful. We were able to make progress towards our own greater understanding of the importance of the Early Years of learning mathematics, and specifically Spatial Reasoning. A number of workable plans to move forwards were "cast", and I feel that these will be acted upon. I understand that the booking process for BIRS sessions has to be made quite a signficant amount of time in advance. It would be very helpful if this could be examined to see if it was possible to shorten the time for both longer sessions and the weekend sessions. The networking potential of bringing experts together is huge, and something that education is gradually picking up more and more from the business world. BIRS can facilitate this process in my opinion, AND actively demonstrate support to and involvement with the early years of learning mathematics.

I made some excellent new contacts. We have spent the day emailing about a joint project, in fact. This was an area I knew little about, but it is an exciting extension of my current work and will enrich it. I have a student who will be able to use the new collaboration that is emerging to enrich her work and make connections to new literature. So, I've only been home 1 day, but already I feel as if it was a great experience that will stimulate research activities.

I found the workshop very helpful. Met amazing passionate people, so dedicated to helping. I am in the Elder Project in Sooke teaching Kindergarten classes in 3 schools and one on reserve. I realize how important it is to include forms of math in language teaching. Children are so eager to learn; they are so very open at that age. I think your facility there is great. Beautiful setting- my first time there, good introduction to the territory.

The recent BIRS First Nations Math Education workshop was unlikely to have very much direct bearing on my mathematical research, but I hope that BIRS will continue to host such workshops, which bring First Nations people into better contact with mathematics, and contribute indirectly to mathematical research, since they begin at the roots, in schools, where we are very much in need of help and stimulus. I found this particular workshop very encouraging, as, apart from the organizers, there were many people present who were keen to spread the word, and clearly able to do so.

This is the second First Nations Mathematics Education workshop I have attended. It was fabulous. The opportunity to collaborate with teachers and elders on mathematical investigations for students was very welcome and would be much more difficult without BIRS support.

Mathematics, Physics, and Engineering, Mount Royal University

The workshop was very useful for the following reasons. (i) I could present my work and get some valuable feedback from other participants. (ii) I met new people who could be eventual collaborators. (iii) I learnt a lot of new stuff from the talks and from the informal discussions.

This was an excellent workshop. And wonderfully organized, as always in BIRS.

I had several very helpful discussions concerning my research program and started a new collaboration with other two participant to the workshop that have complementary knowledge on a problem of common interest.

Mathematics, University of Rome Tor Vergata

This workshop was really useful for me. It was my first meeting in my research field. I am a phD student, and this workshop allowed me to have contact with many other researchers, with whom I hope to begin collaboration. Moreover, the place was the greatest one to do mathematics during one week: all was really well organized, and I spent 5 fantastic days in Banff, with these so beautiful mountains around.

UMPA, Ecole Normale Superieure de Lyon

The workshop was great, lots of very interesting discussions, with input from various sides, theoretical physics, probability, and numerical simulations. Energy transport in one dimension remains a lively subject with many surprises. Concretely, in the light of new numerical data, I am strongly motivated to reconsider the predictions of nonlinear fluctuating hydrodynamics.

I was an organizer of this workshop, and had therefore the opportunity to invite researchers whose works and papers I liked -- even though there were quite a few colleagues who I never physically met before. Needless to say, I had many discussion topics when coming to BIRS, and I looked forward meeting the very specialists of the field to get some feedback on these potential research tracks. I was delighted by the outcomes of these discussions, because, as usual, there are hints, remarks and comments which come to one's mind in an actual conversation, and which do not come out in a more constructed series of emails. In addition, there are also all these questions and issues which are raised at the end of the lectures: some inspired new research directions, some gave me new views of current problems of interest, some allowed me to revisit something I thought was settled, etc. There really was quite a biodiversity of viewpoints between physicists interested in the interpretation of results, mathematicians interest in the formal aspects of the theories, and applied mathematicians concerned about the efficiency and precision of numerical schemes. Also, the more familial size of the workshop and the cozy atmosphere of the place (in sharp contrast with the refreshing climate of the surroundings mountains) definitively triggered informal contacts and spontaneous scientific discussions between all generations of researchers, from PhD student to emeritus.

The meeting was extremely well organised and the new results and new insight will have a good impact on our research. New contacts were definitely made which will lead to further interactions. The meeting helped also my ex-PhD student in deveoping his own future and interactions and I am delighted about this.

Mechanical and Aerospace Engineering, Cornell University

To my opinion the workshop was very useful for me. I heard many new interesting results which impact my and my colleagues research. I met the scientists whom I had not known before and we started our contacts. I hope that we will do together with some of them in future. I do not think, that the workshop affect my job prospects, my student's or my postdoc now, but it may happen later. I heard the talks with the applications of the things which I know to problems which I considered very far from them.

A.Ishlinsky Institute for Problem in Mechanics of Russ.Academy of Sciences

The Workshop was well conceived, bringing together people in fields that are different yet similar enough for meaningful and indeed useful connections to develop. I enjoyed several enlightening conversations, as well as the lectures. The surroundings are magnificent, the accommodation is comfortable, the food is superb, and all the Banff Centre staff were unfailingly helpful.

Physics, University of Bristol, U.K.

A great workshop in a magnificent research facility: compliment to the organizers!

Mechanical Engineering, University of Trento

This workshop was a great experience for me. I got to know many great colleagues whom I had not met before: I knew only two of the attendees previously. I received very good feedback on my talk and enjoyed many of the other talks. The video system was really impressive, especially the lecture being posted so soon after being recorded.

It was a superb week at BIRS. I enjoyed it a lot and I am very grateful for all the new colleagues I was able to get in contact with. Moreover, my personal research activities were greatly influenced, so much that even my PhD students here in Germany will feel it! Thank you for this wonderful week!

Institut fuer Mathematik, TU Ilmenau

Yes, I have benefited by the workshop very much. The program covered rather interdisciplinary subjects. I could lean many new things. I could also start interactions with researches of different disciplines.

Graduate School of Frontier Sciences, Department of Advanced Energy, University of Tokyo

The presentations and follow-up questions/discussions were great resources for participates to know the current research directions and interests. I marked quite a few papers for further reading. The part I like most in attending the BRIS workshop is that I was able to meet different scholars from closed research areas and discuss research problems with them. This is extremely useful when participates are trying to broaden their research interests and seek for opportunities of collaboration. During this workshop, I had some productive discussions with researchers who are working on Hopf algebras, graded Skew Clifford algebras and got to know some open questions in those areas. We discussed problems and possible solutions over the board in those small rooms downstairs. (A great place to do research. The security man was very nice and made us feel comfortable stay after midnight.) Such discussions were very beneficial. I did have new collaboration that originated during the workshop. I will definitely keep these contacts and continue these research communications.

The BIRS workshop talks were valuable in helping me to keep up with current research in my field, as well as to learn some related topics that are a bit further afield for me. I met with collaborators on two research projects at the workshop. Both are projects I have just begun, with mathematicians that I do not see very often, and it was important that I speak with them in person at this stage to get the projects moving.

I enjoyed the conference very much. The networking opportunities were great and I met quite a few like-minded people. Most talks broadened my perspectives and gave me ideas on how to enrich our programs. Very well done! PLEASE inform me about future conferences that relate to mathematics education.

Calgary Bright Minds

I think it is rather the participants obligation to say thanks to the organization for the kind hospitality which resulted not only a pleasant week in a beautiful surrounding, but also provided us a fruitful period of time to inform each other about results we reached recently in this field and gave us opportunity to discuss possible promising directions of further investigations. I am convinced that this opinion reflects not only my personal feelings, I am sure it is shared by the other participants of the workshop as well as. If the other BIRS-workshops are nearly as successful as our turned out to be then you can be duly satisfied.

I am very grateful for the opportunity to attend this workshop which gave me the opportunity to meet old acquaintances, Heppes and Borosczky, and discussing interesting open problems with them as well as hearing much new mathematics and having the opportunity to discuss these with others.

It's a great pleasure for me to thank you for my stay at BIRS. It is very useful to meet people with the same interests as myself. This may sound a highly trivial statement, but it isn't since I'm almost the only one in Scandinavia in the field defining the conference.I had many interesting discussions there and the inspiration received has still not worn out; I'm just now looking into a brand new idea for a solution, at least in low-dimensional cases, of a problem (called Sierksma's Dutch cheese problem) which is strongly related to one of the main themes of the conference.

It is I who should thank you for providing such a marvelous facility in a beautiful setting to conduct workshops. I had never been to Banff before, but I'm hoping that this will not be my last trip.

I had an excellent time at BIRS. The workshop was, as might be expected, interesting and informative, but the infrastructure BIRS provides makes it so much more pleasurable. What's more, it makes it easy to concentrate on the work itself. I had a chance to work with some collaborators, and we fully expect a paper to come out of our joint work.

The workshop definitely lead to new ideas, insights and research projects. Also some new contacts and one collaboration that would not have happened without this workshop. It is very possible/likely that the workshop will have a positive impact on my job prospects but it is a bit too early to tell.

I learned a nice proof about a problem I previously published a paper on. A former student of mine and I obtained a result on a problem presented at the workshop. I had productive discussions with several people I previously did not know well.

The workshop was amazingly inspiring. This happened during the talks and the scientific questionings, but also all along during the discussions in the seminar and over the meals. The atmosphere and service that BIRS are providing are amazing, first rate for sure. I got fresh insights into an old problem (travelling salesperson on grids), due to the interaction with two other participants, one from Canada, one from Spain. It is this international collaboration from various perspectives that makes BIRS a uniquely fruitful place. A new research project may very well result from this interaction. The contact to the colleague from Canada would not have been possible otherwise, I believe.

My participation in the BIRS workshop clearly impacted my current research: it was an opportunity for me to meet with several people (e.g. K. Zainoulline) and discuss new ideas, some of which will be the subject of joint papers. Also, naturally, this major event in the field helps us all to keep up to date with the latest results.

The BIRS workshop is wonderful. It provides me a great opportunity to give a presentation. This is the firs time that I give a talk in a conference. Most importantly, the workshop is a good place to learn new ideas. Although many presentations are professional and difficult to be understood by me, I get a good first impression of many research topics.

The fact is that the goes much beyond the only scope of my research, it is even hard to express it properly in English. Even though I was told that BIRS is one of the most incredible places in the world to make mathematics, I have been still amazed. The natural background, the organization, the setting of this workshop was incredible, and it is clearly the conference where i both enjoyed the place the most and worked the most.

The great environment (research- and otherwise) helped me to focus on a particular problem related the the workshop themes and while still at BIRS I typed up some notes regarding that problem, thus also reviving a collaboration on that topic in the process.

Mathematics, TU Dortmund

I have very recently returned from the wonderfully inspiring and productive BIRS workshop on Lie algebras, torsors and cohomological invariants. I want to thank you most warmly for creating together with your outstanding staff including Wynne Fong, Brent Kearney, Brenda Williams and Caroline Green the extraordinary ideal conditions for collaborative research work and for facilitating up to date quick information about the new results, new developments and new hopes. In particular it was very impressing immediately after a lecture of a participant to receive an e.mail from my graduate student in London, Ontario who was very excited about this lecture and who asked me to recommend him further lectures from the workshop suitable for his current studies and research work. The ease of the use and the quality of recording is remarkable. The hospitality and help of your team in every respect was just great. The workshop itself was superbly organized by Stefan Gille, Nikita Karpenko, Arturo Pianzola, Vera Serganova and Kirill Zainoulline. The lectures were very inspiring and so were the many discussions during lectures breaks,hikes,dining and other relaxing times. Thanks to this conference I began a project with Detlev Hoffman on structure of inseparable extensions and Witt kernels and further possible projects may develop from discussions and subsequent mutual visits with Stefan Gille, Raman Parimala and Kirill Zainoulline. The informative very happy friendly and exciting atmosphere in the spectacular environment was the key to ultimate success of this workshop.

I had a great time at BIRS -- not only were there excellent talks, but there was also some time to continue my research with Arturo Pianzola. In fact, we achieved a breakthrough there for our current research project.

Among the subjects of this workshop, I was very interested in the part concerning torsors and cohomological invariants, as well as on motivic aspects and applications for quadratic forms and algebras with involutions. I was very happy to assist to the very nice talks we had and to learn more on this subjects. I had also a chance to have a lot of conversations with other participants, which gave me some interesting projects, I am currently working on, and I hope this will lead to some new results soon.

IRMA, Strasbourg

I consider the workshop to be a great success. The quantity and quality of young researches and speakers was exceptional. More than half of speakers were young researchers and graduate students. The enthusiasm of the participants was evidenced by the frequent discussions and many questions asked after each talk. I feel that the experience that participants gained during the workshop will prove to be very valuable in their research career and will undoubtedly have a positive impact on the research activity in the area. I think, the idea to bring together people from different areas (Lie algebras and Torsors) was very fruitful and has lead to several interesting collaborations already. I expect that these will grow into joint research projects and publications.

The workshop was a fantastic tribute to the outstanding work of Harold Widom. On a personal note I can say that discussions spurred by the talk of K. T. R. McLaughlin and of P. Bleher on the normal matrix model has already lead to interesting development in the study of universality (bulk and boundary), and I am presently very actively pursuing the topic with McLaughlin (Arizona). Already some results seem to appear. Thus I reckon it was an exceptionally fruitful experience and thank BIRS for the opportunity.

Mathematics and Statistics, Concordia University

This was a very high quality workshop and I learned a lot of new results which will be very useful for my current research. I am in this area for a long time, and I know most of the participants, but there were some new people. It is possible that I will have new collaborations originated at the workshop. The workshop can influence the hiring process which we will have this year at our department. We will see. I think that the workshop will have a significant impact on the area of random matrix models and their applications, in terms of new collaborations, publications, presentations, etc.

The workshop was wonderful. It gave me a chance to catch up and have some very helpful discussions with colleagues, make progress on two current projects with two of the organizers, and present some recent work. It was also a terrific opportunity for my most recent PhD student to present his work and make important contacts which may lead to future collaborations.

Mathematics Institute, University of Warwick

At the workshop the most recent results in our field were reported, an information which otherwise would be obtained much later and only partially. Concrete examples for me are: 1) discussions with Ortmann and O'Connell on Brownian motion in the Weyl chamber, 2) discussions with Sasamoto on duality for ASEP, 3) discussions with Baik, Kazumasa (Baik reported on a new identity for he Airy process, Kazumasa could extract an confirmation from his liquid crystal experiment.) 4) discussions with Corwin on the semi-discrete directed polymer with stationary initial data, 5) discussions with Borodin and Corwin on oblique reflections in the Weyl chamber, 6) discussions with Valko on superdiffusive bounds. Presumably there are more. But these discussions advanced my own research. Item 2 is not applicable. There have been many informal exchanges, which generate a common feeling for separating important from less important items.

Mathematics, Technische Universität München

My participation in the BIRS workshop was a significant event on my current research. Talks and private discussions led me to some informal insights and techniques that are often hidden in the formalities of papers. I look forward to launching a research project related to the meeting and following up on fantastic discussions that occurred at the workshop. I am hopeful that these will grow into new collaborations, which are so important to a young mathematician, such as myself.

The workshop was excellent and it did provide me with opportunities for making new contacts, learning about new ideas, and meeting several mathematicians who I have not met before. There were many opportunities for discussing mathematics. The lectures were great and the informal discussions were extremely valuable. The organization was flawless and the atmosphere of the centre is fantastic.

The workshop encompassed several topics which were either in my area of current interest or near my extended interests. It was a very good combination, and I had the opportunity to meet both collaborators and researchers I had not met before. We will see if the job prospects of my students/postdocs were affected, but they did get the opportunity to present their work.

Mathematics, University of California, Berkeley

This workshop and the nice scientific atmosphere in BIRS allowed me, with my collaborators Professors S. Ibrahim and K. Nakanishi, to complete the final steps in proving the finite time blowup for the inviscid primitive equations for the large scale oceanic and atmospheric dynamics. This is a nice breakthrough result, and we will certainly acknowledge our visit to BIRS in our paper.

Mathematics, University of California and The Weizmann Institute of Science

In the workshop, I listened to several reports I am familiar with and learned some new results and fresh insight; and all of them are useful for my study and research in the future. I also met a lot of outstanding mathematicians in this workshop. I get more confidence from chatting with them.

Thank you very much for supporting our meeting in BIRS this September. The meeting was an absolute success! Just yesterday I received yet another email from a young participant telling me how beneficial the workshop was for him (we will put some of the extracts in the report). It was a very fruitful meeting: new research programs were discussed and what was amazing, some of them turned out to be related in the most unexpected ways! New collaborations were started, the old ones continued, etc. etc. All this would not have been possible without BIRS and your support!

During the workshop I was able to discuss a problem with Prof. Andrew Chermak, which I had discussed with Prof. Michael Aschbacher last year. Some new and unpublished results of Chermak seem to point into the right direction, the workshop was an opportunity to bring the ideas together.

Department of Mathematical Sciences, University of Copenhagen

The workshop gave me the opportunity to learn about exciting new developments in neighboring fields. I also found the time to work together with several of my coauthors on finishing off joint projects.

I found some new, strange examples of non-growing sets in finite simple groups. With Gill, my former coauthor we discussed possible applications of a new growth result he obtained recently.

Discrete Mathematics, Renyi Institute of Mathematics Budapest

I was able to make progress on 2 different research projects, one with Barabra Baumeister, and a second with Kay Magaard. As well, I had preliminary discussions with Tim Burness about a possible collaboration. This was all very valuable and would have taken much longer under ordinary circumstances.

In my opinion, the lectures given at the workshop were very interesting and informative. They covered many different important research topics in the area. The workshop's schedule also provided ample time for me to discuss various mathematical questions with other participants. In particular, I had stimulating discussions with M. Aschbacher, R. M. Guralnick, and M. Liebeck on some ongoing research projects. I will continue working on these projects.

This conference was very helpful for my own research programme! I had the chance to talk with several people, including Micheal Aschbacher, and could ask some specific and some general questions that are not suitable over email. It is only at such high-level conferences like this one that I meet these persons and can talk to them. For instance, and more exactly, the motivation of Micheal's study of the E_6 module was important for me to know, so that I can consider similar applications for my study of the E_7 and E_8 modules.

I was at the Banff Centre for the first time and I was impressed by the surroundings and by the atmosphere on campus. There were many interesting talks and plenty of opportunities to talk to colleagues, so I could make progress in an ongoing project, get to know new people and learn a lot about recent important results in my research area.

This was a an excellent conference including stellar researchers who presented the most exciting developments in combinatorics. Between the talks and informal conversations, several new project ideas came up which may lead to papers. I talked with several researchers in the field that led to several enlightening problems and new proof techniques. I was quite impressed with the conference!

Department of Mathematics, Massachusetts Institute of Technology

During the workshop I listened many very interesting talks focused on the topic of syzygies, where I have worked and I have still a open research plan. I had the opportunity to speak directly with some of the main experts in the area, also about the connection with physics. During my talk I left an open computational problem, and other younger participants considered it seriously and I am now in contact with them. I hope future collaboration with postdoc students will arise fromm the contacts I had in this workshop.

This is a wonderful workshop, I have the chance to talk to the experts about the research I am doing, and hear very useful suggestions and comments from them.

During the workshop, I had some stimulating discussions with participants regarding various problems in nonlinear PDE I am interested in. Many of the talks and remarks point to some possible new research projects in the future.

This meeting at BIRS was quite interesting for me. I knew many of the participants, but a lot of the material was new to me and it will certainly be of inspiration for my future research as well as for the topics I will propose to my students and post-docs.

I'd like to express my gratitude for the invitation to BIRS. I really enjoyed and appreciated this workshop, which I found perfectly organized, both practically and logistically, as well as the location at Banff Center (actually it was my first time in Banff). Most of the talks were pretty inherent to my mathematical interests. Even though no new collaboration has originated during this week, some clues to probable future research projects have arisen from stimulating discussions with other participants. Moreover I've had the chance to talk to best experts in the topics concerning some problem in geometric analysis I'm facing now.

The workshop on conformal and CR geometry last week was very successful from several perspectives. First of all, there was a lot of interaction among the various groups exchanging information on the new directions, and formation of new collaborations. I personally learned a lot about the new operators from Eastwood's survey lectures and from Kengo Hirachi about his approach to understanding the new operator that Jeffrey Case and I are developing. The survey lecture of Guillarmou covers a lot of new ground, and challenges PDE people to develop criteria of existence and uniqueness for the Poincare-Einstein structures. I had also learned about the work of Alexakis/Mazzeo that may be relevant for my own work with Alice Chang. Each time I come to Banff, I have gained new perspective on future research direction and found the environment absolutely stimulating. I would like to thank the BIRS for creating such possibilities for us.

Math Kangaroo Contest workshop at BIRS will impact my future research, since right now I am doing some work about digital signal processing, but it gave me an insight of education. To combine what my background and education, I may get into engineering education. It is about motivation for students and passion of educators. I found it is very interesting and such a wonderful thing to devote yourself into. I may volunteer Math Kangaroo Contest in the future to make a contribution for the kids in mathematical education. I also met nice people from different places and backgrounds with the same interest. I think we will keep contact to each other and the networking will work very well.

Electrical and Computer Engineering, University of Calgary

The organization was great!

Natural Sciences, Southern University at New Orleans

I enjoyed my stay at BIRS very much, everyone on the staff was very friendly and helpful and the conference was stimulating.

The workshop is certainly going to be very useful for the future research of my group. It was a great mix of analysis and geometry and it certainly gives new perspectives for PDEs in a geometric context. The lectures were at a great level, and I had the chance to meet several new people, both junior and senior.

The workshop was very rewarding. The talks were interesting and serval collaborations got started. As always, BIRS staff made everything easy and the setting is beautiful. Thank you very much.

The BIRS site is fantastic and inspiring. The physical layout and the schedule promoted collegial interactions. The meeting was a perfect mix of quantitative experiments and modeling.

University of Pennsylvania

Our workshop turned out to be a remarkable success. We brought together mathematicians and physicists on the one hand and biologists on the other, and the interaction was both stimulating and revealing. We noticed interesting differences in our angles of viewing the problems of tissue growth, our approaches to describing and rationalizing the process, and even the use of terminology. From a personal standpoint, I was delighted to learn of the latest experimental results on the signaling pathways; these will be incorporated into our mathematical model. Our model, imperfect as it seems to us, so impressed the biologists that I was invited to visit a top group in Duke University. This dialog between math and biology has given me several new ideas, and has greatly broadened our vista of the related biological problems. Judging from the enthusiastic (and uninvited) email messages from the attendees that have come to me in the past few days, I think many share my impression that this workshop has provided a rare opportunity for inter-disciplinary exchange, and will have potentially far-reaching benefits for research on both sides, e.g. by forging new collaborations. Besides, I was interviewed by the Banff Centre Communications Officer and her staff since the topic of our workshop captured their interest. The interview will appear in the Banff Centre website and through a podcast. Thus we might have done a bit of outreach in bringing our science to the awareness of the public. Thanks again for your aegis of this wonderful gathering, which has given the attendees new ideas that we now rush to implement.

I thought the workshop was a useful forum to learn about new research being done in our field. Many of the results were unpublished and I was quite pleased with that. Also, it was terrific to have such an international representation at the meeting. I did renew contacts with people that could turn into potential collaborations in the future.

It was very relevant and could make new contacts with people working in the same field. These contact will probably lead to new collaborations and future work. I had new insight, that may have some effect on my current research. No new hiring or new projects so far though.

Although I could not attend the workshop due to visa issues, I enjoyed the presentations. Thanks to the live streaming of most of the talks. I am now aware of many interesting findings which would have otherwise taken much longer time.

Department of Environmental Health, Harvard University

The format, and in particular the way that participants are housed and take meals together in more-or-less isolated surroundings, is a great strength of these meetings and an important factor in their productivity. The talks and more importantly the discussions which went on throughout the week, both scheduled and informal, gave me new insight into various definitions and open questions, with direct impact on ongoing work of my own. A new project was also started at the meeting as a direct result of informal discussions with two other participants.

Chemistry, University of Sheffield

I participated in the BIRS workshop on rigidity this summer. During this meeting I reconnected with two old colleagues and made new connections with 4 or 5 new ones. This may ultimately lead to very fruitful new collaborations. Working with one of the collaborators allowed us to combine techniques from our individual works that should lead to a characterization for global rigidity of periodic frameworks. Additionally, at this meeting, various parties that have worked on complex and hyperbolic rigidity were able to get together to finally figure out what was collectively known and collectively unknown. This will greatly help progress on these questions.

My visit to BIRS saw me concentrating on developing an existing collaboration into a new area, and it provided an ideal environment for this. We certainly developed some new insights - difficult to yet know how significant these will be.

This was a useful workshop, with new insights and at least two new collaborations started. How they finish is yet to be seen. I do believe the workshop made a positive impact on the field.

Mathematics, University of California at Los Angeles

I found the event extremely interesting and helpful, primarily for three reasons. Firstly, the technical presentations from experts in their respective areas gave me a lot of new ideas, some of which I am certain I will be able to consolidate through collaborations. Secondly, this was an extremely useful networking event that gave me the chance to meet important female figures in the IEEE community. Finally, I just had a really great time!

My participation in the BIRS workshop allowed me to make important contacts with people from my research area, as well as to be able to get significant insights of their current areas of research which provides me new interesting ideas for my job. Also the contacts I made during the workshop may help me through my career with postdoc opportunities or joint projects.

My time at BIRS was really pleasant: it was useful for my mathematical projects and all the activities that your centre offers were absolutely amazing. I agree with you in thanking the organizers of the last week: Han Peters and Erlend Fornaess Wold. I hope to have other opportunities to come to Banff International Research Station.

I found the workshop very interesting and learned some results that I did not know. Also, I started some new collaboration with researchers met there, which I think will produce interesting new results.

Another superb BIRS conference, bringing computational mathematicians together with number theorists and topologists to drive experimental and theoretical work on a circle of questions which were complete mysteries only a few years ago.

The conference gave me a unique chance to interact with some of the leading experts on several topics that I have been very interested in recently. I left Banff with several promising ideas/projects and a deeper understanding. I can't wait to visit again!

Mathematics Institute, University of Warwick

My participation in the BIRS workshop did indeed impact significantly in my current research: it provided great stimulation to graduate students that attended, and it initiated a new collaboration (on the topic of application of integral equation methods to eigenvalue problems, a rather novel approach) with two other participants. Interestingly, subsequent to the initiation of this work, I had two independent requests from colleagues at engineering departments at Caltech (Chemical Engineering and Electrical Engineering), whose needs required exactly the type of method we developed as a result of these interactions in Banff: use of commercial software for these problems had proven unsatisfactory, and our new methods provide the needed accuracy and efficiency. We have thus started three independent highly interesting collaborations as a result of the interactions initiated during the BIRS workshop. Additionally, participating students had a tremendous opportunity to meet and interact with some of the most active scientists in the field. In all, this was an extremely useful experience. Thank you so much for making it possible.

The workshop was the opportunity 1) To present a joint talk with my collaborator M. Costabel and to re-launch this project (Cosserat spectrum), after a good reception by the audience, 2) To meet and have scientific exchanges with J. Ovall, on adaptative eigenvector computations, 3) In connection with point 2), to build a benchmark page http://perso.univ-rennes1.fr/monique.dauge/schroedinger/benchmark.html

The discussions outside of the lectures refocused me on certain key questions such as what are "points" in the Delta flat topology and what kind of lifting properties do we have in the differential setting. This was quite useful.

(1) I learned recent results on descriptive set theory and von Neumann algebras, and I found them quite interesting. Among others it was particularly nice to get to know logicians (Farah, Hart, and others) working on applying model theory to von Neumann algebras. I would like to keep discussing about this topic with them. I enjoyed talking with Andrew Toms on central sequence algebras and feel the different flavor of central sequences in C* context. (2) It was nice for me to have had an opportunity to talk in front of experts. It is definitely good for improving my presentation skills and getting to know experts in the relevant field. (3) I found talks on Polish groups quite interesting, and I would like to know more about them. I did not expect to hear such talks, because the workshop were only for set theory and some directly related analysis.

The conference was not exactly in my field of research (which would be more on the set theory side), but it certainly allowed me to understand better what is currently done in operator algebras, and to meet some people from that field. I appreciated the effort that some of the speakers (not all) from functional analysis put into being understandable from the set theorists. On the other hand, quite a number of pretty close colleagues were also present. That allowed a good balance between discovery and discussions on more precise subject. The latter opened at least three seemingly very interesting research tracks, and will very likely impact my research very soon. All in all, that was a very pleasant stay, and if the results I expect from turn out to be confirmed, it will also have been a very profitable one.

It was my second time attending a BIRS workshop and again I found the experience very enjoyable and extremely mathematically productive. The wide range of expertise of the workshop participants was a particular benefit of this meeting: I found the interactions with specialists in the structure theory of von Neumann algebras particularly useful, as well as learning significantly from experts in model theory and descriptive set theory. With Andrew Toms and Wilhelm Winter, I managed to make progress on the regularity conjecture for nuclear C*-algebras. We are currently preparing a paper on this topic in which it will be a pleasure to record our thanks to BIRS.

This was one of the best workshops that I have ever participated in. The format of having the day split into half the time lectures, the other half problems sessions made it possible to really absorb the material discussed in the lecture. In a typical workshop that I have participated in, having an opportunity to really understand the material has not necessarily been a given. This past week I have expanded my background of number theory into the realm of the methods to solve Diophantine equations. Any opportunity to broaden the scope of one's field is always valuable, especially in such a well structured workshop. I had the opportunity to meet a number of number theorists at this workshop, for the first time, which was really great.

In my PhD I am specializing in the modular approach to Diophantine equations which was one of the topics taught in the school. This way the summer school was very useful to me to get to know other techniques to solving Diophantine equations and to see how they interact with the modular approach. This was something that was already in my plans but this school allowed me to do it in a fast and systematic way. I also met several people I wouldn't have met otherwise and it is not that I had started a new collaboration during the school but I am sure that some collaboration will happen in the future. Also, I arrived two days earlier in order to meet with another mathematician that was in a BIRS workshop the previous week and stayed late in order for us to collaborate.

The content of the workshop was very relevant to my dissertation research. By participating in problem sessions and talking to the lecturers I got several new ideas to try on a problem I'm thinking about for my thesis. I met several people at the workshop which I'm very glad to have come in contact with, since we work on closely related subjects. I do expect to have future collaborations in research with some of them.

The workshop gave a good overview of the various tools that mathematicians use today to solve Diophantine equations. There were also exercises that helped us become comfortable using these tools. I gained a good perspective on how Diophantine equations can be solved, and I had a really good time.

The workshop was great, with all of the talks being interesting and very helpful. The methods to solve Diophantine equations that were shown were all among the most powerful known today and it was nice to see them explained by some of the people that developed them. I believe the workshop will have a noticeable impact on my future research.

The BIRS Summer School on Contemporary Methods for Solving Diophantine Equations was outstanding. I got more out of attending this summer school than any summer school or conference I have attended so far. The lectures were really interesting and well presented and the problems were challenging and very enjoyable. I learnt a lot by working on the problems in small groups and discussing the finer points of the lectures with other participants. The BIRS is the perfect location for such a summer school. The Banff Centre is very well set up and the surroundings are beautiful. Many thanks to the organisers for doing such a fantastic job and I hope there will be more events like this in the future.

This BIRS summer school on Diophantine equations has been really fruitful for me. I do not work with Diophantine equations, so it was great learning all the modern methods to solve them in one place. The lectures were brilliant and beautifully interrelated. The problem sessions were challenging and it helped in absorbing the lecture materials. I also liked very much the idea of recording the lectures and it will certainly be useful for people who could not attend this summer school. The Banff Centre's hospitality has been awesome and I really thank all the organisers for all their efforts. The experience from Banff will definitely be helpful for my future research.

I work on building algorithms to automate the design of integrated circuits (IC). Even though I am a practitioner, I use mathematical theories and have to follow the new developments in mathematics to be able to apply them in my work. The participation in this workshop had a significant impact on my research as I became familiar with the newest research in Robust optimization and also had time to discuss my issues with the best in the robust optimization field in the great mountain setting and I have two ideas to work on that I think will result in high quality publications. In addition, I met Dr. Bertsimas from MIT and Dr. Stephan Wild from Argonne National Laboratory. These new connections might result in collaborations in the future.

I think the workshop has been well organized and serves well the needs of the optimization society. The value proposition of the workshop is well presented, where the panel discussion was very thought provoking. The workshop certainly provides a great start for researchers in optimization society to re-focus on the real value that robust optimization can bring to the industry. I benefit a lot from the workshop, seeing how the trend of robust optimization may evolve.

The following points made the meeting in Banff useful to me: 1) New contact with brilliant people I did not know before 2) New knowledge of the discipline I am interested in

Mathematics, SISSA

It is a very nice meeting. We know the recent progress in the optimal transportation theory, in particular, its connection with differential geometry. During the conference, we have the chance to discuss with the colleagues the various applications. These would give the fresh ideas in some "old" problems...

It's a such wonderful workshop, the organizers has done a superb job. BIRS is always a great place for mathematicians exchanging and generating ideas. Myself this time benefited from the workshop, I and my collaborators worked out something we struggled for last two years. It was in Banff last week we were able to put all pieces together. Thank you again, BIRS!

I enjoyed most talks and fruitful discussions.

The participation has been particularly fruitful, with a significant impact on my current research.

The workshop expose me to the most recent progress in the area of optimal transport. I get to know many experts in this area and problems that they are interested in.

Mathematics, stanford university

The BIRS workshop will impact my research in many aspects. In addition to contribute to my current field of interest, it opened new possibilities along with new collaborations.

The workshop brought to my attention a new aspect of the mathematical treatment of turbulence that will be part of my research in the next future. Moreover, I had the opportunity to meet people who worked on fluid models with an approach complimentary to mine; with one of them I started a collaboration.

This workshop gave me a chance to meet with many well-known people in this field. I discussed with these people about the future direction of my research and got great advices and comments from them. I think that I will have many new outcomes based on this workshop in the future.

The workshop stimulated me in continuing with the topic on which I gave a presentation and it gave me some useful directions of further research. The informal way in which the workshop was held is a very good way to stimulate interaction between the participants. There was ample time for discussions during and between the presentations. Since the presentations could also be followed by others through the video stream, I also got useful and stimulating comments from non-participants.

The BIRS workshop has been a great experience for me. I could present my latest research results to a group of people closely connected to it. This is not the case in many conferences. In this sense, I think it is a great idea to organize this kind of meetings. On the other hand, I met and shared experiences and impressions with people that I already knew but also with some others that I just knew by their names. So, for me this gathering has been a great opportunity to make new contacts. I am sure that this will positively influence my ongoing and future research.

Heat and Mass Transfer Technological Center, Technical University of Catalonia

It was great to know what the leading experts in the field are working on, and so the current hot topics. The station provides also a good working environment.

I think that the Banff Centre is a magnificent institution which give great opportunities for people to refresh their minds in order to get re-inspired.

The workshop was an excellent opportunity to get more familiar with recent developments in my research area as well as with new interactions with other areas. It was an occasion to meet researchers from other areas that I did not know yet or that I just met once so far (at the meeting at BIRS in 2010) and to learn more about their work. I appreciated the fact that the workshop had a well defined focus, and I found that the average level of the talks was unusually high, both regarding contents and exposition.

During this workshop, we have lots of interesting talks. Moreover, I talked to some colleagues, and the discussion helps me to solve a particular problem in my research. In the same time, I have the opportunity to ask problems to top researchers, like Professor Ringel and Krause, and so on.

School of Mathematical Sciences, USTC Hefei

The subject of the workshop were links between representation theory, singularity theory and non-commutative algebraic geometry. The talks were especially chosen to relate at least two of these subjects. My own expertise is in singularity theory. I learned a lot about new connections, in particular to non-commutative algebraic geometry. This is a subject which I am not familiar with. I got useful insights into this subject and my attention was drawn to relations which I was not aware of. I found particularly interesting a talk of Kazushi Ueda where he gave an general picture of mirror symmetry throwing also a new light on my joint work with David Ploog. Important for my current research was also the fact that I met my coworker Atsushi Takahashi (Osaka) among the participants and we had the opportunity to discuss our ongoing research. I benefitted very much from the workshop and I hope that there will be another workshop of this kind in two years.

The workshop was, like the years before, an excellent selection of talks from algebra and algebraic geometry. My private opinion was, that the workshop covered many new developments, that I took a lot of profit from, and also gave some introduction into recent important developments. In particular, the talks of Ragnar Buchweitz I should mention here. I hope that series will proceed and we can meet again in two years at this excellent place.

The workshop was very stimulating. I have learned many new ideas from people in various research fields. During the workshop, I was able to find a possible interactive project with people in another research field. I hope it will work!

This was my first experience as a participant of a workshop in BIRS. I met new people and talked to some well known figure (that I didn't really talked to previously) in my area. As a postdoctoral fellow, I even found some opportunities to extend my postdoc. for next year. The organizers gave me the opportunity to give a talk. I had some very constructive comments related to it. They will be useful in my current and future works.

The participation in the BIRS workshop has been very useful for me since I established new contacts and I discussed with experts about my current research projects.

Matematics, Università di Torino

I did not think about calibrated geometry in Pseudo Riemannion case before the first talk in Banff and I believe some result of Blaine and me should also work for this case. It was a very exciting workshop which broadens my view of math much.

Math Department, Stony Brook University

It was an excellent website and I had lots of valuable ideas to use in the classroom. I am hoping to hold my first math fair next year in March. I will let you know how it goes.

The workshop definitely had a positive impact on my future research activities. I already have 3 PhD students taking up different aspects of research problems that are a direct result of my participation at this meeting.

Statistics, Columbia University

The topic touches on fundamentals...how to deal with data that are incomplete or partially inaccessible...a challenging question. The opening sessions gave a very clear over view of the topic and indicated the challenges. The venue and the organization and the associations provided the essentials. There seems now from the workshop to be an essential resolution which was sketched in the final summary session, central to this is the BIRS workshop style and the BIRS organization.

It was great to meet so many people working in the relatively small field of composite likelihood methods. I think that the workshop was very successful in clarifying the progress that has been made in this subject over the past few years, and highlighting the large number of open questions that remain. I have written down pages and pages of new problems to think about, many of which hadn't occurred to me at all before I attended this workshop. As a PhD student I felt that I was treated no differently to the most well known and respected professors - everyone seemed to be judged not on who they were, but on what they had to say. With the reasonably small numbers, I think I got to talk to just about all of the other participants, many of whom had very interesting suggestions for new ways to tackle to problems I discussed in my talk. Thank you BIRS!

The workshop was excellent in the sense that I met very interesting and influential people in my discipline but also got informed for ongoing research on the field. It also boosted new collaborations which I find very promising for the future!

Dept of Statistics, Athens University of Economics and Business

This was my first scientific visit to BIRS and I thoroughly hope it will not be my last. I have nothing but admiration and the highest esteem for the organization, the concept, and the way everything is so efficiently run. Friendly staff, a stimulating natural and built environment do everything to inspire creativity, to use a tag line of the Banff Centre. The research interactions, formal and informal, will have a lasting impact on many people's scientific research, including mine. The Banff Centre, and BIRS as part of it, is the modern-day version of the most splendid concept of "desert" that scholars and monks alike sought in medieval times, and that can also be found in some traditional universities, such as Oxford and Cambridge. It reminded me of the "Chartreuse" in France, where the monks retreated in a superb natural environment to devote themselves to their most beloved activities. The Banff Centre has the additional advantage that the seclusion is wonderfully married with the proximity of downtown Banff. I am ever so grateful for a wonderful experience.

I-BioStat, Hasselt University & Katholieke Universiteit Leuven, Belgium

Our workshop was outstanding, and I started at least one new project, and continued on two others. The talks were very good, there was lots of time for discussion, and we all felt we were making real contributions to an important area of research. My graduating PhD student got great exposure to the leaders in his area, which he found inspiring. Even better, he got some leads on postdoc opportunities that he would not have had. I met several old friends and made some new ones, and came home feeling intellectually enriched.

The workshop is very valuable to my current research. A nice collection of talks has updated me significantly the current status of the research progress on composite likelihood methods. With no doubts these heard new ideas, new methods, and new results will impact my pursuit in future research of composite likelihood methods. I am once again convinced that composite likelihood methods will continue to attract a good deal of attention in statistics and have profound impact in theory, methods and applications.

I think this workshop could likely have a substantial impact on the diffusion of composite likelihood methods in statistics and related disciplines. I enjoy the talks and learn much about a diversity of applications of composite likelihood methods. Furthermore, the workshop gave me the opportunity to meet coauthors and discuss about ongoing and new projects.

Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University

One thing that the workshop did was mix geometers and topologists. This was good for me (as a topologist) in two specific ways. I met my collaborator Fuquan Fang (a geometer from China). We put the finishing touches on a project and started a new one. I met and had interesting discussions with Claude LeBrun who suggested the problem of determining which 7-manifolds admit Einstein metrics. I have an ex-student (Diarmuid Crowley) who is the world's expert on the topology of 7-manifolds, and I will talk to him about this interesting mix of geometry and topology.

We had a great week at BIRS. Our report will fill you in on some of the new developments both from the talks (most are available on video), and from the lively discussions among the participants. Several of my own projects got a boost from talking to people at the meeting, so that was a bonus. This was the first time I experienced the new TCPL facility for the lectures. It is perfect, and the video recording produces a surprisingly good quality image and sound. As usual, the local organization by Brenda Williams and Brent Kearney was excellent.

The BIRS workshop "Geometric structures on manifolds" was wonderful. As with all of my BIRS experiences, I came away from this workshop invigorated and with new mathematical perspective. This workshop, in particular, was great in that it introduced me both to people and to ideas with which I had little prior exposure. I was impressed by the speakers and the diversity of mathematics presented at the workshop. People made a real effort to communicate with mathematicians outside of their normal circles; a rare phenomenon at many conferences that I attend. As usual the organization, the food, the technology, and the accommodations were outstanding. BIRS is a truly special place.

Mathematics, Michigan State University

First thank you and the organizing committee for the invitation to the BIRS workshop. I enjoyed it a great deal both mathematically and environmentally. For me this is a extremely smooth conference from arriving at Calgary and leaving Calgary. The instruction is clear, on-time and short enough (so that we have patience to read it completely), this takes care of my arriving at and leaving my BIRS room. Since this is my first time to Banff, I like the format that all our food are taken care of so that we do not waste our time on this front. Another thing I like is that the noon time break is long so that we have time to mingle together. Mathematically I extremely like the diversity of the topics of talks and the quality of the talks, though I am a geometric analyst, I benefit from quite a few talks, in particular the talk by LeBrun on the classification of Einstein 4-manifolds with complex structure, the talk by Hillman on the homotopy type of geometric 4-manifolds, and the talk by Biquard on desingularizing Einstein orbifolds. I enjoyed the talk by Baldridge a lot. Out of talks I asked Bryant some questions about the deformation of G_2 manifolds. He also explained to a group of people about his on-going study of Bonnett theorem in affine spaces, I liked it. I also talked quite a bit of math with Fang. To me this is a very fruitful conference, I can not ask more from it. Here I want to say again, thank you and the other organizer and BIRS.

As a participant, it was nice to have the talks restricted to 45 minutes. With that length, it's easier to pay attention. The facilities, scenery, and food were all magnificent. In terms of professional development and networking, I feel that my presence at these sorts of conferences is crucial. I already have a postdoc, but I will be moving overseas, so I need to form my North American connections now. The talks were very nice, and it was helpful to see several talks in the same subject area, namely Spin7/G2 manifolds. Most valuable were my interactions with other participants. I met several colleagues and big-name researchers, and caught up with several friends. I had many conversations which were very helpful. Foremost, I am currently working on a project about Chern-Simons theory, which was informed by my discussions with Paul Kirk and Matt Hedden. Also, I had a nice discussion with Robert Bryant regarding an identity I had discovered. The conference was very productive, smooth and enjoyable. I hope to return soon to BIRS!

Mathematics & Statistics, McMaster University

The workshop was a great place to meet people working in an area somewhat different from mine, but still related. I also had an opportunity to work with a colleague on a joint project that was conceived at another BIRS meeting last year.

Attending the BIRS workshop "Open Dynamical Systems: Ergodic Theory, Probabilistic Methods and Applications" was a perfect opportunity for me to reacquaint myself with a subject that I worked on some years ago, and I found the meeting very inspiring, informing me about many aspects of the subject that I can't tell I was thoroughly aware of (such as the developments in numerical computation of spectra of transfer operators and the applications to metastable systems). For renewing contacts and forging new ones, these workshops are ideal, and it helps me in my activities as referee, journal editor and mathematician in general.

It a very interesting workshop. I met with many people working on similar problems as myself. I learned about new problems and some new results. I have a chance to talk to people I would not probably meet otherwise. Three of my former PhD students also attended, so it was great to meet with them. And Banff is a wonderful place. I greatly enjoyed the walk on the Sulphur Mountain.

Department of Mathematics & Statistics, Concordia University

Many thanks also for the opportunity to stay and work at BIRS again. It is always a very enjoyable stay. As a matter of fact, the workshop initiated a collaboration with Kathrin Padberg-Gehle and Shane Ross and I am very excited about this. We are going to apply techniques on the detection of global bifurcations based on transfer operator techniques to fluid motion. We suspect that this might be a new way to, e.g., predict certain phenomena like vortex splitting and thus have interesting applications in weather forecasts.

The BIRS workshop 'Open Dynamical Systems: Ergodic Theory, Probabilistic Methods and Applications' offered the opportunity to become familiar with many recent results on topics in both abstract and applied ergodic theory. I think that without this opportunity it would have been very hard if not impossible to have gained a reasonable understanding of some of these latest results, which might influence my future research. Also, the workshop facilitated communication with the other participants. Although it is very hard to say a few days after the workshop, how many of the new ideas- my possible collaborators and I came up with during several conversations -will end up in publishable papers, I am very hopeful in this respect. Furthermore, some of these possible new collaborators, are researchers that I would have not been able to discuss at large with, otherwise. I am a postdoc and no, I do not think that the workshop influenced my job prospects. I think that the workshop made realize once more that there are many open questions in both abstract and applied ergodic theory that are worth exploring.

Very nice workshop, lots of good talks with interesting differences in background, bravo. Banff is a wonderful place.

I have been to BIRS on several occasions, attending quite different programs on varying topics. BIRS has always offered a highly-stimulating intellectual environment, without fail. It was exactly that way this time, as well. However, this was the first time that I had organized a meeting in BIRS myself, and so I had a first chance to see more closely how the institute is run. It is truly an amazing undertaking, with wonderful, dedicated staff, in [as always] spectacular surroundings. I am deeply grateful for the opportunity to have been there. At the end of the conference, several people expressly told me how energized they felt about their research program. I too feel that way. Almost everyone that I spoke with told me how they found the new video technology truly remarkable [it truly is].

Mathematics, University of Utah

My participation in the BIRS workshop was very helpful to my research. I learned about new developments and recent results, and I could discuss with major experts in the field in a very relaxing atmosphere.

Mathematics, University of Kansas

The fact that the workshop's main subject was restricted to Stochastic Analysis and SPDEs made that almost all talks were very interesting and definitively provided me a fresh insight in the topic. I also had the opportunity to discuss with some of my current collaborators about our ongoing projects, some of which are related to the content of some of the workshop talks. In general, I found the workshop's format very convenient and it has positively influenced my research projects.

I appreciate very much to listen to new problems related to the area in which I work. In particular I think to the problem of parabolic Anderson model that I was not familiar before. It has maybe helped a PhD student of mine to have a new significant contact.

I like every aspect of this workshop. The level and areas of mathematics I had seen in this workshop is excellent.

It was worthwhile for me. In particular, for doing more attractive works in visit other partners.

Attending this workshop was very helpful for my research. During the week I was able to spend time working on some examples with participants Geraschanko and Satriano which we hope will lead to a joint paper on integration on toric stacks. I was also able to meet Amalendu Krishna and learn about the use of A^1 homotopy techniques in cycle theory on stacks. This too looks like it may lead to a joint project. Finally, the conferenece gave me a chance to work with ongoing collaborators Jarvis and Kimura and an opportunity to present some of our joint work on $\lambda$-ring structures in orbifold K-theory. This is the second Banff conference I've attended. At the first conference in 2008 I met Jarvis and Kimura and we began a collaboration that continues to date. Once again, it looks like I'll be able to gain new collaborators by attending a Banff conference. I think that having participants share a dormitory and common meals definitely helps foster mathematical discussion.

Thank you very much for the great job that was put forward by BIRS to make the workshop such a wonderful experience. I agree that the organizers put together a set of very interesting and stimulating topics. I indeed brought back several ideas that I plan to investigate in the next few months.

We had a fantastic workshop on Monte Carlo methods. The atmosphere is very conducive to discussions and planting the seeds for new research directions and projects. I am currently working on two ideas. They will however take time before they become publications.

Department of Computer Science, University of British Columbia

As always, I fully enjoyed the privilege of attending a workshop at BIRS! If you do not mind, here are the links to my reflections on the meeting: http://xianblog.wordpress.com/2012/03/20/banff-worshop-birs-12w5105-meeting/; http://xianblog.wordpress.com/2012/03/21/banff-workshop-birs-12w5105-meeting-2/; http://xianblog.wordpress.com/2012/03/23/banff-workshop-birs-12w5105-meeting-3/; Once again, the organisation was flawless, the facilities beyond the reasonable, the new feature of videotaping the lectures brilliant (I have had several feedbacks from people who were NOT at the workshop), and the atmosphere at the workshop particularly congenial (a. everyone attended a. every talk and there were only two talks that I found superfluous). Incidentally, I took the opportunity of sleepless nights at BIRS to write the following http://arxiv.org/abs/1203.6249; although it is not related to the theme of the workshop.

A lot of talks were very interesting and informative for me. I have met several people interested in the theory of Elliptic algebras (I worked at this theory during ten years, see Russ.Math.Surveys 57 (2002) 6 or arXiv:math/0303021 for a survey). I have made an informal talk for them and we had a lot of discussions. When I returned to elliptic algebras (preparing to my informal talk and during our discussions) I realized that there are some possible directions of research there and I plan to start these research.

Mathematics, Brock University

This conference was very influential for me to learn many subjects related to my area but not exactly the same area. In particular, results from a view of representation and non-compact symplectic varieties were impressive for me. Bedies these, I was happy to hear from Doctor Gunnar Magnusson (a participant) that my talk is also applicable to construct non-K\"ahler manifolds of intertesting nature. This was very impressive for me, as I never thought about applications in such directions.

Graduate School of Science, Departmenrt of Mathematics, Osaka University

The conference enabled me to continue some collaborations in progress and made me aware of some new work that is closely related to things I had done years ago on the C(alpha) spaces and may lead to additional results. In addition I was able to talk to a prospective postdoc, Dosev, and we subsequently completed arrangements for him to spend next year in Stillwater.

Mathematics, Oklahoma State University

The workshop kept me up to date with a field of research close to mine. I had new contacts that I wouldn't have had otherwise. Feedback about my talk helped me improve a paper.

Mathematics, Texas A&M University

During the workshop, I had an idea for a proof that originated a paper that is almost ready now (tentatively entitled "A new proof of Pietsch's composition theorem"). Also, a question after my talk made me realize a result that followed from what I already had. Moreover, another comment made me aware of the fact that I was looking at a situation well understood in categorical Banach space theory; I am now in the process of incorporating these categorical methods into my research. Thanks to the workshop, I got invited to give a talk at another conference. I don't think this would have happened if I had not been there.

Department of Mathematics, Texas A&M University

The workshop gave an impulse to my current research, essentially by talking with people I already collaborated with, as well as opening possibilities of organizing future events with some people I met at the workshop.

I would like to thank you and the organizers of BIRS 12w5019 for doing an outstanding job on organizing this workshop. It is perhaps the best conference, evaluating facilities, attendance and scientific program, I've ever attended. Best regards,

I learned that a problem I was very much interested in on commutators had been solved by Matt Tarbard. Since he did not know that his example solved the problem, it was good that I was in the audience when he spoke. I was struck by the depth in the development of the infinite dimensional theory. Due to the work of the Argyros and Odell-Schlumprecht schools, we have a completely different picture of the structure of general Banach spaces than we had a few years ago. It was gratifying to see how many good young people are working in the field.

1. I worked on current projects with current coauthors. 2. I discussed possible future projects with recent coauthors. 3. Most importantly, I met new people with whom I discussed possible future projects. 4. The whole atmosphere was very inspiring.

I found the workshop very inspiring and thoroughly enjoyable. There was a good mix between people specializing in various directions of Banach space theory. I definitely made some new connections and learnt some new results relevant for my ongoing research.

The workshop was excellent in every way. The talks were of very high quality. I was introduced to the latest directions in research in Banach space theory. I also had the chance of interacting with colleagues to discuss possible joint projects.

In general, my participation in the BIRS workshop has only had a positive impact upon me, in every aspect. Indeed, i was given the chance to get more familiar with fields i was not involved in so far, as well as offered the opportunity to become better informed about methods and results concerning my main field of study. Since i am a young researcher, the workshop was an excellent way for me to meet other researchers, young and more experienced alike, which led to various scientific discussions, offering the prospect of new collaborations and papers. Since i still have a few years ahead of me in order to obtain my Ph.d, my job prospects may not be a matter of primary concern to me, nevertheless i believe that coming in touch with all these members of the scientific community will have a positive influence on this aspect in the future.

The workshop was very fruitful for my current and future research, thanks to new methods I got more familiar with during the workshop and new research projects which I started there - also in collaboration with other participants. I appreciate very much the talks delivered during the workshop as well as the possibility of discussion with other researchers I don't have opportunity to meet often.

The participation in the workshop was very stimulating for me. I learned about new advances in the field. In particular, after the talk of Christian Rosendal, I realized that his new joint paper with Ferenczi is related to my old work on isometries. I started a new cooperation with Steve Dilworth and we expect to answer some of the problems described by Ferenczi and Rosendal in their paper (some of these questions are quite old, but the new approach of Ferenczi and Rosendal shed very good light on them). Without coming to the workshop it is highly unlikely that I would have known about this modern approach and that I would contribute to the solutions of these problems. I expect that Steve Dilworth and I will have a paper about this coming out in the fall. I also had a chance to discuss another research project with Gideon Schechtman and Bill Johnson. This project was not directly related to the theme of the workshop, but it was a great opportunity to meet and be able to discuss the problem in person. This will also lead to a joint publication with Gideon Schechtman. Seeing many young people at the conference was very valuable to me as a member of the hiring committee at my department. We may be able to offer some temporary positions to some people I met at the workshop, this is still uncertain in the present economic situation, but I am working towards it.

This was a splendid conference,one of the best I've ever been to, and I've been to a lot! All of the talks were at an exceptionally high level,and well illustrated the great diversity in our field of research-hats off to the organizers! Informal discussions ,some with people I'd never met, produced very stimulating questions and new directions of research. In particular, i'd like to mention the following questions which emerged during the workshop. Let X be a separable Banach space with the bounded approximation property. Is the double dual of the space of compact operators on X non-separable? An affirmative answer would show there cannot be a reflexive Banach space with the approximation property such that every operator on it is compact + scalar multiple of the identity. But here is an approach,which in any case points to a new fundamental object associated with this problem. Suppose X has a monotone basis,and let Se denote the space of sequences tending to zero,which act as bounded operators on the basis by multiplication,endowed with the operator norm. A beautiful argument shown me by Ted Odell shows that every sequence tending to 0, of bounded variation belongs to Se. Is Se^** non-separable? Even if one could simply show that Se is not quasi-reflexive, the above mentioned problem about reflexive spaces would have a negative answer. The conference greatly helped me crystallize my thinking concerning the Invariant Subspace problem, Although I believe i am close to a negative solution to the Hyper-Invariant subspace problem (for Hilbert space), I understood during the conference that results I've already obtained yield a new direction in research in classical harmonic analysis,of independent interest. Furthermore, i discovered formulations of a "suitable" class of Banach spaces for which my ideas would work,if they carry through for Hilbert space itself. Finally, I started a joint project with a young guy from Canada,concerning the following open problem If an operator on a complex Banach space has the unit circle as it's spectrum,but no point spectrum,does it have a log? i conjecture that my recently discovered weighted invertible bilateral shift is a counterexample. Of course the organizers created a marvelous,warm atmosphere during the entire conference. a most enjoyable and highly stimulating experience!

Department of Mathematics, University of Texas at Austin

My participation helped established a new cooperation on a paper to be written. This collaboration would most probably have taken place also without the conference but it would have been much more time consuming and painful. I think the participation of my postdoc, Detelin Dosev, (and of Dale Alspach, Bill Johnson and myself) helped him secured a job at Oklahoma State University next year.

The Banach space conference was excellent and I had the opportunity to learn about new developments and talk with mathematicians I haven't met before. I also worked with a colleague present at the conference on a project of common interest and we arranged to meet again over the summer to continue our collaboration. The setting of the conference, the organization, accommodations, facilities, are all very very good.

I enjoyed the Banach space workshop enormously. The program was mathematically exceptionally strong with a number of very deep and difficult results on constructions of some special spaces with very few bounded operators and on related structures in arbitrary Banach spaces or in algebras B(X). Several "more fundamental" general lectures presented perspectives (and some technicalities) of the theory of infinite-dimensional Banach spaces in the last several years and pointed out directions for the future. These lectures were complemented by shorter technical talks illustrating concrete recent results and methods, given by a number of obviously very talented researchers of younger generation. Most of talks were on a highest scientific level, and all were interesting. I could not pick talks to miss would I want to "play hooky" so as a result I attended all of them (!). To tell the truth this was quite an unusual experience for me. I discussed that with some other "senior" friends and we were all very impressed especially by a quality and a number of young people in the area. I was happy to see breakthrough developments of recent years, especially the construction of Argyros and Haydon which has as a starting point Bourgain--Delbaen's space from the late 1970's. In Banff i started to understand some other potential ideas closer to my own research. It was a very stimulating meeting.

The workshop: Banach space theory did have positive impact on my current research. There were several new results about closed ideals and commutators of operators on certain Banach spaces. These are the topics I am currently working on. I also got to know some people working on Banach space theory from Europe whom I never met before.

I had conversations with Vern Paulsen, Marius Junge, Benoit Collins, Toby Cubitt, Matt Hastings and Andreas Winter that I want to follow up on. It's too early to know if these will lead to new results, but Vern and Marius told me about areas of math that are far enough outside of what I normally do that it would be very interesting if a new connection were made. Also, I mentioned an open problem and Matthias Christandl came up with a partial solution to it. And I made some small progress on an open problem of Magdalena Musat and Uffe Haagerup, and helped simplify a result of Carlos Palazuelos. In general, the workshop left me with some small concrete new pieces of knowledge, and a large number of promising directions that I want to pursue. Overall, a great way to spend a week!

My time at BIRS was great. The workshop brought together people in operator theory and quantum information theory. I am a quantum information theorist, so this was a great chance to learn about some problems in operator theory that are closely related to quantum information theory. I have to admit that I learned about and started thinking about one of the biggest open problems in operator theory, the Connes embedding conjecture. To be honest with myself, I probably have very little chance of making progress on this conjecture, since it has been such an outstanding problem in operator theory. However, since I learned about it, and further learned about various related conjectures in quantum information theory and about how to cast the embedding conjecture as a certain natural problem in information theory, I have been very interested in this problem and it has captured my attention. So, perhaps something good will come out of this---unlikely, but if it does it will be very nice! I also had a chance to present some topics that I am working on, and got some outstanding feedback from different perspectives than I am used to. This has already benefitted my thoughts on these problems, and some of the insights from my discussions at BIRS will likely benefit a paper that should be finished fairly soon. The organization was outstanding in every aspect. The venue is excellent, the rooms are great for discussion and the TCPL is a wonderful spot.

The workshop was very important to me, and I think also to Gdansk group of quantum information. Thanks to the workshop I have become aware about a rapidly growing sub-community of quantum information that uses powerful mathematical tool to solve problems that have been so far intractable by our community, including myself. If I did not participate in the workshop, I might have not noticed this big trend for quite a while, which would seriously affect me and my group. I have realized that I have to learn these techniques, and also I have actually treated this workshop as a first course, asking all the time, more or less stupid questions, trying to get as much as possible. I am going now to invite several people that presented their results during the workshop to my group, so that we can learn more. I feel, that this workshop will prove very fruitful for several projects, which our group in Gdansk have are just starting. I am therefore extremely grateful to BIRS as well as the organizers of the workshop.

University of Gdansk

The workshop remains an important condensing point (and is quite unique for the operator algebra QI interaction), and initiates or boosts a lot of collaboration, I had lots of important talks lat week. I will make sure we mention the workshop in resulting papers.

As on previous occasions, this BIRS workshop was a hugely pleasant and intellectually stimulating experience. I got some nice ideas to take away from it, on which I'm working now. I found particularly useful the "open problems" session, during which I posed a question, and was delighted to learn some of those of my colleagues. I think the whole thing was a great success and helped bringing two sub-communities closer together, with potentially significant impact in the future.

Just to let you know that the program was very successful and stimulating for my research. I hope there will be other such opportunities for Combinatorics on Words. I thank you for all the work you do.

This workshop certainly inspired my research. Most participants shared their work in progress stressing open problems they feel important and directions they hope promising. I appreciate the informal atmosphere which allowed people to speak about topics where they do not have any tangible results (yet), which is usually not possible on conferences. The workshop helped me to clarify several subject areas suitable for Ph.D. students. I have met people with whom I had been considering some long term research goal for some time, therefore this helped to move them a step forward. Finally, I got involved in one or two new open problems during the workshop.

This workshop allowed me to discuss my research with other mathematicians interested in similar topics. I am shifting the direction of my research slightly as a result of the many talks and informal discussions I had with my colleagues at BIRS.

Mathematics, Northwestern University

This was a very focused workshop, and the level of the discussion was unusually constructive and to the point. I learned much that I did not know and which would not have been uncovered with a broader thematic coverage. This will surely affect my future research in many ways.

Participation in the BIRS workshop was extremely helpful for me. Being an outsider to the field of left-orderability helped to make me aware of the important questions and gave me some new ideas to think about. Furthermore, I was able to meet many new mathematicians that I had not met before and was thus able to learn a great deal of new things from them; there was also a lot of opportunity to speak more with people I had already met - it was particularly helpful to have so many of them all in the same place! I also started a new project with someone based on the discussions that were facilitated at BIRS, which seems quite promising.

Yes, the BIRS workshop was very productive for me. In my talk, I said slightly jokingly, no doubt Dave Witte Morris (one of the participants) should be able to finish this off using his techniques. However Dave made a very clever comment in my talk, and then we got together and finished the problem off. I believe we have proved a significant result, which we wouldn't have done without the workshop. At this time I'm writing a joint paper with Dave.

Great chance to exchange ideas with other experts. Several new ideas and probable collaborations. Many of my (former) students and postdocs were there and gained a lot from the experience.

Mathematics, University of Chicago

The workshop brought together around the orderable groups people from different fields ranking from low dimensional topology to algorithmic group theory, through the dynamical systems. The quality of the lectures as well as the conversations among the participants were exceptional from my point of view. It is a bit early to say how this workshop will influence my research. The only concrete fact in this direction is a draft of collaboration with Cristobal Rivas. However, the amount of information I learned from the lectures and the conversations as well as the new contacts I made during the week will definitively help me in my research, but I cannot predict how and when.

IMB, UMR 5584, Université de Bourgogne

We had an extremely productive meeting. Although I was originally concerned that we had only a half workshop, I now realize that it was in many ways an advantage to have a more intimate group. We had a very good mix of old hands, younger mathematicians and graduate students -- female experts and persons from as far as Japan, France and Chile. Even less than a week after the workshop, I know of at least two publications which are direct results of collaboration last week at BIRS -- by Dave Morris (http://arxiv.org/abs/1202.4716) and Patrick Dehornoy (still in progress). Other people collaborated in small groups working on aspects of the subject of our meeting, between talks an in the evenings. For myself, I spent virtually every free hour in a new collaboration with the Harvard grad student Thomas Koberda on an open problem regarding the space of orderings of a free group (not yet solved, but we're still hard at work on it). I would like to thank the staff at BIRS for helping to create an environment in which mathematicians can maximize their research interaction. It was such a pleasure!

University of British Columbia

This was a very productive workshop for me, leading to new results, a new collaboration that I expect will lead to a paper, and learning about a result very closely related to something I had recently done with a lot of potential for cross-pollination.

Department of Computer Science, Yale University

Being at BIRS was a wonderful experience: The wonderful surroundings, the convenient facilities, and the warm hospitality of the staff has made the stay very comfortable. (Similar thanks go to the Banff centre staff, in the recreation facilities and the dining room.) For me it was first and foremost an opportunity to catch up on interesting research in my area. But it was also an opportunity to create new research: With 11 of my collaborators attending the workshop, I could make progress on several papers that I am writing (in one case, a presentation of the work by one of my coauthors has helped to find new applications). I also had a chance to describe some fresh results to relevant researchers and get their feedback. Finally, I got started on one or two new research directions.

I formed new collaborations during the workshop and started working on two new projects with researchers I met there. In addition, I gained new insights about several topics that were discussed, which will definitely impact my research.

This was an extremely productive workshop for me, maybe more so than almost any other workshop I've been involved in. The workshop was not quite in my area, though I have expertise in general randomized techniques. I was able to get feedback and encouragement from experts on shared memory computation on some half-baked ideas that I came with. An expert in this area whom I had never really talked to joined me and a couple of others in a collaboration which extended one of those ideas and will likely lead to a publication. On another idea, I received encouragement to publish and names of people to contact who might know more about the problem. Finally, working there with someone I often collaborate with, we came up with ideas which I think can be used to solve a major open problem.

Department of Computer Science, University of Victoria

My participation in the workshop had a very concrete impact on my research. Indeed, at this workshop I began a collaboration with Luc Devroye on a problem related to my talk. This resulted in some new research that has now been submitted to a journal, and which can be found on the arxiv http://arxiv.org/abs/1202.5945.

I worked closely with Chris Laskowski on a continuing project related to my talk and made significant progress. The talks of Kim and Scow helped clarify a further paper I am working on. The paper of Hils may resurrect a project that has been on the back burner. Discussions with Tanevic and Haskell were helpful with my editorial responsibilities with the Bulletin of Symbolic Logic. Many other talks provided inspiration and insight that should be helpful in the future.

Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

On February 2009 when a similar Classification theory (model theory) Workshop was help at BIRS, I talked with Dr. John Goodrick for the first time. Then we promised to start a research project together. Some months after, he and I and Alexei Kolesnikov met together and started a research project: A category theoretical understanding of model theoretic amalgamation. This project was very successful and resulted as a joint paper accepted in Israel Journal of Mathematics. The project was continued and we are now developing model theoretic homology theory connected with our earlier work. We already submit our some 70 page homology paper, and continue to work on extending the results in the paper. All these fruition began with the mentioned BIRS Worshop. Moreover in the new BIRS Workshop (Neostability theory), I and John met again, and we work and talk together. On Thursday evening in the lounge, we finally resolve the problem how to compute the higher homology group of a canonical higher groupoid. This is a big jump toward the study on computing higher homology groups and on solving our related conjectures. We express our deep thanks to the meeting organizers and BIRS administrators and staffs who support all this happening. Finally I want to mention the following. During the workshop, Dr. Joon Kim (who graduated in 2011 under my supervision) gave a talk. Many audience including scholars from Bogota, Colombia seemed impressed by his talk. And I just received an email from Joon Kim that he will get an official postdoc offer from Universidad de los Andes, Bogota, Colombia. This is a great help as well to the beginning-stage Korean logic community. Joon Kim is the first Ph. D. ever produced in South Korea specialized in mathematical logic. So his success as a research scholar is crucial in growing Korean logic community.

Mathematics, Yonsei University

First of all many thanks for giving me the opportunity to take part in this conference, in such a beautiful, inspiring and well organized environment. It gave me the opportunity to have constructive talks with at least two people coming from very far away, which is not always as successful when writing emails. It also allowed me to meet new researchers having close interests to mine, which could be a first step towards future projects. Of course, it also permitted to have an up to date overview of what people are looking at in my field of research : I did learn a lot.

Thank you so much for having me to BIRS for this workshop. The talks were excellent and the workshop was very well organized. The Banff Centre is a fantastic place to have this type of conference, and I will definitely highly recommend it to others, as well as hopefully attending or organizing future workshops myself! Thanks again very much for you wonderful hospitality.

Thank you very much for organising these fantastic workshops at BIRS. I had a great time in Banff last week. I have learned about new mathematical models in my field, I have met great researchers (such as Prof. Jose Carillo de la Plata - whom I would have not met otherwise), and started a possible collaboration (and a possible paper). BIRS is a fantastic place to do research (to start new projects, to establish new contacts, ...). I was honoured to be invited to attend this workshop, and I am already looking forward to my next visit at BIRS.

This workshop was addressed very timely and interesting problems and is certainly going to have significant impact on my future research. It served excellently in forming closer relations with key players of the field I had hardly opportunity to meet otherwise.

I was one of the few engineers among mathematicians and researchers from other fields working on the topic of swarms or multi-particle systems with local and non-local interactions. I learned a lot about the view and aspect researchers from other fields have. It helped me form new ideas for expanding my current research. I also had the opportunity to communicate our results and views. I believe that it was a very useful interaction.

Electrical and Electronics Engineering, Istanbul Kemerburgaz University

It was a very nice and interesting workshop. I particularly enjoyed hearing about the work of up-and-coming junior people. A junior colleague (postdoc) and I also started a new collaboration with one of the participants.

Mathematics, University of Arizona

I was very fortunate to attend the BIRS workshop on interactive information theory. As a computer scientist I don't usually get to interact with information theorists and electrical engineering researchers. This workshop provided me with such an opportunity. I have been working on applications of information theory in the field of computational complexity -- a subarea of computer science. The workshop has really impacted my research agenda in two ways. It exposed me to new ideas from information theory, which allowed me and my students to make progress on the problems we have been working on. At the same time, it made me aware of the problems and challenges in information theory to which the techniques we have been developing can be applied. I hope BIRS will hold another workshop in this area in the future years.

The workshop was very beneficial in getting people from related fields together. This is valuable to our community as it created a better awareness of the specific problems people are currently addressing, and available mathematical methods to address these problems. It also gave me an opportunity to meet and exchange with new researchers in my area. This too is of great value. I think that the BIRS workshop will have a definite impact on the research in our area (interactive information theory). It may take a few months or a couple of years for the seeds planted during the workshop to come to fruition.

The wonderful BIRS Workshop on Interactive Information Theory (Jan 16-20, 2012) afforded several intellectual benefits. I met and learned of the research of several computer scientists who work on areas related to my own but who normally do not attend the same meetings as I do. The tutorial lectures organized by Profs. Devroye, Khisti and Blake, as part of the Workshop program, were very useful. Several new and exciting ideas were discussed. My student, Himanshu Tyagi, gave a well-received one-hour tutorial which, I think, will have a beneficial impact on his future career in academia.

Electrical and Computer Engineering, University of Maryland

This has been perhaps one of the three best scientific gatherings I have ever been to. The small number of selected participants and the focused topic provided opportunity for intensive discussions. After this workshop there is a potential for at least 3-4 new collaborations, which is excellent and rare in other conferences.

Electronic Systems, Aalborg University

The participants, and the organisers in particular, have really appreciated the BIRS experience. The organizational help we received and the facilities and location were all outstanding, and allowed us to concentrate on the meeting goals and scientific discussions. We are currently in the process of gathering all the material of the discussions/talks into the basis of our report which we look forward to sending to you in due course. Please pass on our sincere thanks to the BIRS team.

We really enjoyed organising the workshop with BIRS. The organisational help we received was outstanding and made it easy to setup the workshop. The facilities at BIRS are excellent, very well suited for such a workshop. So overall we were able to concentrate on the science instead of lots of administrative issues. I believe the workshop brought together scientists working on different approaches towards quantum devices, which triggered quite a few new directions to explore. We are currently in the process of compiling the report describing the overall results in far more detail.

The conference was wonderful. I found out about a new model for dynamic networks that my student and I will examine this semester. I also got caught up on several areas that I had not followed closely for the last few years.

Statistics, Duke University

The reception some of my ideas got has motivated me to work faster on some of them with a view towards publication. They are joint work with a PhD student so I'm hopeful it will help his career as well. Certainly, I made new contacts (I even got invited to be an AE for a journal!) and kept up with developments in the work of some people I follow. Of particular note is that one researcher gave a talk and I didn't know she was working in that area (longitudinal) so I have asked her to read over a section of a review paper I'm working on and she agreed. That will be helpful to me. The workshop left me with the overwhelming feeling that sparsity issues, which were a major topic of the talks, has been pushed about as far as it can be. It told me we need new ideas since we've hit the limit of the old ones. This is particularly true in the statistical side of data mining and machine learning. I think I saw some glimmers of new ideas that might become important in the future, especially predictive criteria ...but only time will tell. I think we need another conference!!!

My research recently stalled and this workshop was a lifesaver! It was very stimulating to meet with other people in my research area and to hear what they are doing. I'm now much more enthusiastic about some of my ongoing projects and thinking about new ones. This is quite a small research area and it's easy to feel isolated and somewhat alienated from the mainstream of the discipline. A small workshop is ideal for bringing potential collaborators together and renewing existing ones.

The workshop was small enough for me to get to know all the participants in person. It was interesting that some presenters are using the same datasets with mine, taking different approach to research to a different finding. I could also hear a presentation which supports our methodologies. In summary, the workshop was very motivating for me to proceed my research in this field.

I saw several talks that change how I think about topics I will teach. I also got some good research ideas that I started following up on while on the trip home. In addition I met some up and coming Canadian statisticians that I expect to keep in touch with over the years.

Statistics, Stanford University

The conference is great. Talks are interesting and I learned a lot. I like small conference like this one so that participants can interact well with each other.

I am very pleased I was invited to participate of this workshop. The level of the talks and interaction with colleagues were excellent. For example, Matias, Yumi, and I had very nice discussions with Alejandro Murua (from U. of Montreal) We believe we started a very nice future collaboration. I also had fruitful discussions with other participants including Steven Wang and Bert Clarke. The facilities and accommodations were outstanding. Thank you VERY MUCH.

The program was excellent and all of the talks were of high quality. A lot of fresh ideas were conveyed and exchanged during the workshop. I liked that all the talks were plenary, so that I would not worry about missing any of them! I truly enjoyed the communications after the talks, informal chats in the evening, and conversations with other participants during the meals. Actually, some new research ideas came up over my conversation with a speaker, and we started the collaborations now. Statistical learning is an important research area under rapid development. This workshop was just on time. It was at a proper scale, making it very easy for participants to talk with each other for a long time.

Mathematics, University of Arizona

Actually, I've been to BIRS twice. The first was in March 2010. There was a little hike up Tunnel Mountain with Philip Candelas that led after dinner to some scribbling on napkins. A year and a half later, I was there again for the Hodge theory and string duality workshop, and during that week the finished paper went on the arXiv. A lot of work took place in between, of course - but it was nice to have both bookends firmly rooted in the Canadian Rockies.

The BIRS workshop last week was indeed useful and stimulating. It is wonderful that BIRS is able to sponsor this sort of interdisciplinary research that spans art and math. There was a great mix of folks with varying backgrounds and we all gained enormously from the interactions. I made a number of new contacts, learned of many references to follow up on, and came back with interesting new ideas to pursue. So I expect the workshop will have a significant impact on my work both as a mathematical artist and as a designer of The Museum of Mathematics, which will open next year in New York City. I should mention that the workshop organizers were fantastic. They invited a great set of researchers and kept things moving very well. Everyone had opportunities to present and interact. In addition, the facilities at BIRS are just ideal for this kind of work. The meeting rooms, the Corbett Hall lounge and hotel rooms, the cafeteria, and the wider Banff Center facilities leave no room for complaint. Finally, I must give the highest praise to Brenda Williams, who went beyond the call of duty again and again to arrange for our special needs. It is such a pleasure to work with her. Her energy and good will are outstanding. Thank you BIRS!

Our BIRS workshop was incredibly useful to me. Example outcomes include: - Initiated a joint paper with two of my colleagues from the workshop - Am currently writing a proposal with another colleague from the workshop (Although we have collaborated before, we had not thought to write this proposal before talking at the workshop.) - Got new data to work on from another colleague at the workshop - Have proposed collaborating on an educational project to try to teach math to high school students using the ideas of stylometry of art with yet another colleague from the workshop - Am leaving feeling more inspired than I have in a long time Thanks for your support for our wonderful workshop!

Electrical, Computer, and Energy Engineering, University of Colorado at Boulder

The impact for my research will probably be very important: meetings with people I had not met previously, who will potentially be new collaborators, and also new ideas for research that popped up after discussions. The very unusual mixture in this meeting (mixing people from maths and from arts) was also very enriching. BIRS is an unique place for this type of meetings: I have not seen such experiments elsewhere, and I hope that the experience will be renewed, and the idea will be picked by other conference centers! My warmest thanks for this very special and exciting meeting!

Mathematics, Université Paris est Créteil

Thank you very much for your good support. Although the outside temperature was low for me, I felt warm. I enjoyed the lectures of course. I also enjoyed the talks and discussions in the restaurant and in the residence. They were stimulating. Thank you very much again. Please give my best regards to all your staff.

The BIRS workshop will be very important to my current research. It offers fresh insights in the intersection between math and art, an area that not many people are working on but has high societal significance. By looking at what others in this interdisciplinary field are doing, I will be able to better determine future directions. I have got new contacts that I wouldn't have had otherwise.

College of Information Sciences and Technology, Penn State University and NSF

This workshop was a huge success, and every participant has come to us and said it. It was easily the best workshop I had gone to, mainly because of the diverse participants. The workshop has focused on arts and mathematics, as the title has suggested. In the end we have gathered a number of mathematicians whose research areas are in art stylometry, and a few others whose research focuses on art generation. There are also three participants whose work focuses on music and mathematics. In all, all the talks showed a good balance of mathematics and arts. The interaction was unbelievable, and it was so much better by the beautiful surrounding and great food!

The opportunity to gather together a few dozen researchers is priceless. I am employed at a university with no other researcher in my area and so these opportunities to collaborate with and learn from my colleagues is immensely important.

School of Electrical Engineering and Computer Science, Oregon State University

On behalf of my co-organizers, I would like to thank you and the staff at BIRS for all the great work you (and they) did before and during the workshop. Based on our own experience and the feedbacks we have received from the participants it was a great workshop and everything went very smoothly. People liked the venue, the rooms were excellent, the food was very good, and the staff (in particular Brenda) made sure everything was going well. I am not sure we could have had asked for anything more. I The workshop provided an excellent opportunity for many participants to do research collaboration and many of my colleagues liked this workshop so much that they have suggested we should do this again. And that's what we plan to do in a few years; hopefully this time we can organize it in a warmer time of year :-) Once again, we thank you, Wynne, and other BIRS staff for giving us this opportunity.

This workshop was outstanding. It fused ideas from complexity theory lower bounds, and algorithmic upper bounds very nicely. Top attendees and a couple real surprises (some significant and surprising new results, ef Chuzhoy and Moscovitz's lectures). I cannot think offhand how this could have been done better.

Mathematics and Statistics, McGill University

As a researcher working on black holes, BIRS workshop has had very positive impact on my research. I was introduced to some of the hottest research topics by very renowned black hole physicists. Discussions with some of the participants were inspiring. The very friendly environment of the workshop helped lots in developing interpersonal relationships with scientists I already knew before or just met there. Generally, it was a great source of enthusiasm.

Our BIRS workshop on Black Holes was extremely successful. This was a joint activity of 3 theoretical physics institutes: ITP of UofA (Canada), APCTP (Korea), and Yukawa ITP (Japan). It was really international: The meeting attracted leading experts in the field from 10 countries. As a result we had very fruitful and informative discussions of the exciting and intriguing problems of the physics and mathematics of black holes. I must say that the staff of the BIRS helped us a lot both at the stage of preparation of the meeting, as well as during its work. All the participants enjoyed very much a friendly atmosphere of Banff Center and BIRS. I would like to thank you and all the staff of BIRS for your cooperation and help.

This was a very well organized and balanced workshop. Most participants were there for the full duration, which meant that discussions could progress and evolve over the week. Although I was familiar with the punchlines of most of the talks, there were a couple of talks on subjects I was not so aware of, which was great, as well as getting some of the details and nuances of work I was more familiar with, which greatly enhanced my general perspective. Finally, the time allowed me to make some good progress on a current research project, stimulated by the discussions and talks taking place.

The workshop was great. I could refresh myself, updating on current status of various interesting subjects of research. In particular, the presentation by Matt Choptuik had some relation with a work I'm doing with a collaborate. It was quite useful. Discussions with Emparan, Lehner and Unruh were also very helpful for extending my understanding on the evolution of the Gregory-Lafflamme instability.

Supercomputing Center, KISTI (Korea Institute of Science and Technology Information)

I had many stimulating discussions with other participants. Some of them might start new collaborations. Thank you for providing very nice atmosphere for scientific work.

This was a splendid workshop. The interactions among all the participants were extremely cordial and informative, and it seems clear that some of the discussions will lead to full-fledged collaborations. For example, some of us are currently continuing discussions initiated during the workshop over email, and these may well lead to some new results worthy of publication. I wish to thank you for your support, and for making the workshop possible.

Now we are starting a small project stimulated by the discussion during the workshop. Hopefully, we will soon write a short paper on it.

Yukawa Institute for Theoretical Physics, Kyoto University

Three years ago, at the BIRS workshop "Black Holes: Mathematical and Computational Aspects," I gave a talk on the black hole solution in the Randall-Sundrum scenario. There, I insisted that the solution is unlikely to exist judging from my numerical result. This year, at the very same BIRS workshop, Prof. Don Page gave an evidence for a solution of large black hole in the same scenario. This talk was best (at least to me) because it raised my curiosity to that problem again. Also, I could discuss with many researchers on this issue, which would be valuable to my future research. I would reconsider that problem again to clarify what is the real solution space, although it may take a year.

Institute of Particle and Nuclear Studies, KEK (High Energy Accelerator Research Organization)

Dear Organizers of the Workshop [11w5011], I would like to comment on my experience visiting the above mentioned Workshop. Besides the fact, that being invited to a Workshop at BIRS is already a great pleasure (as one speaker mentioned: is one of the things a mathematician should do, as in normal life one should plant a tree..), I am very glad having had the opportunity to attend it. I would like to summarize my experience in the following items. - It is always a pleasure to be in a place, where one feels oneself welcomed. This is the case for the whole BIRS (installations, personnel, et cetera). This being naturally the basis of a pleasant stay of any kind, which in our particular case certainly contributed to the effectiveness of the Workshop. - The not so compressed schedule enabled us, the participants, to speak about our research interests in a less rigid atmosphere than within the talks themselves (the given schedule being certainly the "golden ratio", since on the other hand I would have liked to give a talk, as certainly others). For example, I got to know Prof. R. Coulangeon, who got interested in part of my research and is going to invite me to Bordeaux (France) to talk more precisely about the relations between his and my work. I discussed also with Prof. G. Nebe on a problem which was already pointed out to me by Prof. B. Venkov some weeks ago in Aachen. We will pursue this investigation further. - Specialized Conferences or Workshops help younger mathematicians, I mean 'not so experienced mathematicians' (as is my case), to extract the main problems in the area, which may orient ideas and research. Despite the mixture of the two main groups in the Workshop, this was certainly possible in my case. These two groups were, in my eyes, not too far away from each other, so that the mixture was in the end somehow homogeneous. I take the opportunity to thank again Prof. Schulze-Pillot for inviting me and make this extensive to the other three co-organizers. Yours sincerely, Juan Marcos Cervino

The organisers did a good job at gathering people working in different directions (algebra, analytic number theory) and many of the lectures were aimed at a broader audience than the specialists. Even though e-mail is now at our disposal, the informal aspect of face to face discussions is still very frutiful. I was happy to be able to have such discussions with old acquaintances of mine, whom I do not meet so often, and also with a few younger people. As usual, presenting one's research helps clarifying one's mind. The slides I have left on the website (in one of the official languages of Canada) may serve as a light introduction to a nearly finished paper (written in another official language of Canada). There were at least two suggestive comments at the end of my talk, which I keep in mind.

The conference resulted in new contacts that I would not have had. In fact, I met one person I have been waiting to meet for a number of years. I am very pleased about that. The conference was excellent for me.

It is always inspirational to be part of a BIRS workshop. I can't say yet what new mathematics I will do as a result, but I learned quite a bit about subjects that are close to my current interests and I met many old friends and others I'd known only through their publications. The physical surroundings are spectacular and that alone makes the trip worthwhile!

Mathematics, University of Illinois

The workshop gave me many new insights into research of colleagues that are scientifically nearby, but also to colleagues from other nearby disciplines. I think the goal of this workshop to bring together different groups was perfectly achieved. Moreover, my own current research has been influenced a lot by the discussions to colleagues at Banff. Several new results will be published that are influenced from these interactions; some in collaboration with other workshop participants.

My participation in the BIRS workshop did impact my current research in the following ways: Many of the number theoretic problems I work on, eventually lead to problems about lattice points. However, so far I had rather little interactions with the "lattice-community". Thanks to this workshop I met several people of this circle (Kumar, Nebe, Scharlau, SchÃ¼rmann,...) from whom I definitely benefit a lot for my future research, and it seemed also that some of the techniques I developed have been of interest for these people. Not unlikely this will lead to new collaborations. With Jeff Vaaler we discussed a refinement of Schanuel's theorem based on a careful analysis of the height zetafunction, and again, this could lead to a new project.

I attended a "calculus teaching workshop", which naturally did not impact my current research. However, the workshop allowed me to see different ways to teach calculus, it made new resources for teaching calculus available (through a sharing of materials of the participants), it introduced me to many colleagues who teach calculus and with whom I can "network" in future, and it inspired me to strive to become a better calculus instructor. It was a great workshop for me personally, not just because of the ideas I encountered and the contacts I made, but also because of the stunning setting of BIRS. I am very grateful to BIRS (and its funders) for enabling this workshop.

Sciences, University of Alberta, Augustana campus

I found this very interesting and this is the first time I interacted with other calculus teachers. It was refreshing to see that we are not alone and that we all have the same concerns. The heads up on Math 31 is also very useful. I am glad I made contact with Mont Royal and I hope collaboration can start soon.

Centre of Science, University of Athabasca

This workshop impacted my research by giving me an opportunity to learn about many areas of number theory that I was quite unfamiliar with therefore expanding my knowledge in this field. My particular project in the group I worked with had only a small overlap, and I was able to learn about quite a different branch of number theory altogether, yet still having connections to my research. I had worked with each of the participants in my group for the first time, creating previously nonexistent contacts. Our group hopes to produce a few papers related to the work we began during this workshop. My job prospects have certainly been increased. I learned about industrial positions that I was largely unfamiliar with, which have a great similarity to academic jobs. Overall, it can't be emphasized enough how amazing it is to work with strictly women in the field for a week. It is such a pleasant atmosphere that is rare to be involved in. In fact, I have only been in such situations at WIN1 and WIN2.

Although I am just a graduate student, I hugely profited from this experience. It was valuable to get to know experienced researchers but also fellow graduate students, where some future collaboration might evolve. I was pointed towards possible research directions in my field by our group leaders. It was also very interesting to get some insight in other projects and fields which are not so much related to my subject.

The BIRS WIN2 workshop was wonderful. BIRS provides a phenomenal environment for doing research, especially in small collaboration groups, so it was ideal for the format of our workshop. At this workshop I co-led a new collaboration group to address an open problem in arithmetic intersection theory. Our group consisted of myself and 2 NSF postdocs and 2 graduate students from Harvard, MIT, and Brown. We were trying to prove that the Bruinier-Yang and Lauter-Viray arithmetic intersection formulas agree. During the workshop, we partially proved this result under some extra assumptions. We came up with a plan of how to extend the proof and lift these assumptions, and we plan to continue the collaboration over the next few months to finish the proof. This collaboration will result in a joint paper which will either be submitted to a journal or will appear in the WIN2 proceedings volume. This paper will help the group members' careers and job applications, especially the students. I think the collaboration group will help empower the students and the postdocs and may lead to further collaboration projects between group members. For example, after the last WIN workshop, one of my group members did an internship at Microsoft Resarch working with me, which resulted in two additional papers. This time I expect one of the postdocs to visit me next summer at MSR to start another project. A number of students from other groups also asked me about internships at MSR and about how to get funding to continue their WIN collaboration groups. We also used some time in the evenings at the conference to meet and plan for future conferences and the extension of the Women In Number Theory network. We selected organizing committees for future WIN conferences, selected editors for the proceedings volume, and got volunteers to set up the WIN web page, distribution list, and discussion group. It was great fun! Thank you so much for hosting this conference and for the memorable opportunity to take advantage of the BIRS research environment!

Cryptography, Microsoft Research

The Banff WIN II provided an excellent opportunity for me to meet so many good female number theorists, in particular some young talented ones. As a female mathematician, I know it is not easy to survive in a world which is still largely dominated by males. The Banff WIN II helped us to know each others' areas, to build a good connection that is helpful for finding jobs or promotion. It also helped me to introduce my research program to a boarder audience. I am very delighted to work with my group. I am sure the collaboration we started last week is just the rich beginning.

Mathematics, Iowa State University

New contacts, research project and collaborations. Useful informations on job prospects. Got support for the choice of pursuing an academic career.

The week at BIRS was very good for me to think about new problems, (remember the format for this was different than the usual conferences) focus on getting to know the state of the art and see what possible progress could be made. It is fantastic that such facilities with international participation is available in this part of the world.

As a result of the WIN2 conference, I have started a collaboration with new collaborators on an important project in my current research area. We already have some new results, and many new ideas for further results. These collaborators are people I wouldn't have otherwise worked with, but they bring important new perspectives and insights from related but slightly different fields to the project. I expect the collaboration we have started to result in several papers.

The workshop served to re-frame the results of my doctoral dissertation in therms of embodied cognition. That is actually helping me in the writing of a paper for the conference of the Psychology and Mathematics Education international group.

The workshop was really excellent, with a focus that was narrow enough to provide real opportunities for research synergy but broad enough that one was not seeing "the same people, one always sees." The talks of Rotger and Darmon suggested a research project that I could undertake with them, and with a postdoctoral collaborator, Kirsten Wickelgren.

The workshop has exceeded my expectations. The program was carefully thought out, balanced current results with some background material and was of exceptionally high level altogether. A mixture of current results and recent work were reported which informed me and broadened my understanding of the current state of the field. I returned home inspired by the great mathematics I have learned. The facilities and staff were, as always, superb. It remains to congratulate BIRS and the organizers for once again putting together a great workshop

Mathematics and Statistics, McGill University

One of the main topic of the workshop was strongly connected with my recent work and thus the impact of this week on my research has been great and wide. I heard about many related topics and see what people are currently doing in related areas. I also met other matematicians and started thinking about a possibile collaboration with one of them.

Mathematics, Universita' di Padova

During the workshop I got to talk to some of the people working in similar areas as my own. Apart from talking and working with current collaborators, I got the chance to start working in a new project with another participant. Hopefully this will yield some exciting results in the future!

Mathematics, Columbia University

I enjoyed myself a lot. Fun and educational. Keep up the good work! Thanks for running such a nice collection of programs.

I would like to thank you for running such a great program. I enjoyed the BIRS workshop tremendously, in content and in environment alike!

This has given me some new insight and new problem ideas in this area, and I think it will influence my research for the next few years. I met many people and got some new tools to tackle these problems.

Toyota Technological Institute at Chicago

I think in summary it helped a lot to feel the culture of my discipline. As a PhD candidate who had not done much research, it is hard to comment further. But I think it will help me a lot in the future.

Mathematics, Stanford University

A little over two years ago when I was coordinating with other co-organizers to file a workshop proposal, we knew that the particular area of mathematics we were working at that time would grow and produce many interesting results. The actual outcome of the workshop was far beyond the boundary of our wildest imaginations. Originally we thought it would be nice to have a few review talks that would summarize what had happened in the last two years. When the workshop date was approaching, it became clear to me that all talks would feature the most up-to-date and on-going research endeavors. All participants contributed to creating the atmosphere filled with a high level of excitement. Spontaneous discussions took place everywhere, during the breaks and meals, and the night times. Speakers have shared their energy and enthusiasm with the audience. Everybody was invited to have a glimpse of future with the speaker. Physicists proposed new conjectures and challenged mathematicians. Mathematicians responded with new insights, new understanding, and even new conjectures that do not follow from the physics predictions. Often essential questions and constructive criticisms erupted during the talks. The topics discussed were rather diverse, as evidenced from the list of talks. Yet there was a strong backbone that united the theme of all the talks. A characteristic feature of our workshop was the energy of young participants (20 graduate students and postdoctoral scholars) and many first-time participants of BIRS events. I believe the lively event of our workshop that exhibited the excitement of research frontier influenced and engaged these young participants. I myself was able to learn a huge amount of new ideas. Mysteries are deepened. Yet more understandings are developed. I was able to launch two new collaborations during the workshop, which would probably have never taken place without the BIRS event. In short, the workshop was a phenomenal success.

Mathematics, University of California, Davis

I found the scientific content of the workshop really excellent. It was one of the most interesting workshops that I have attended recently. Though there is no direct outcome in terms of new results and/or papers that I can report already, I had plenty of very interesting and useful discussions and hope to continue them since I invited about 5 or 6 people I met there to visit me in Amsterdam next spring.

I benefited a lot from this wonderful workshop. This is no doubt one of the best workshops/conferences that I have ever attended. It is a rare chance to meet so many world leading experts in the field. It exposed me to interesting new problems and I cannot wait to start working on them.

Mathematics, Harvard University

I have started a new collaboration in my research area as a result of my trip to BIRS. This collaboration happened with a question posed during my lecture. It was really gratifying to be exposed to the best research in my field! There was such a feel of creativity motivated by the excellent research talks as well as by top of the line artistic performances. I enjoyed watching native Canadian dances and a wonderful music performance.

Statistics, Columbia University

As an organizer, I didn't give a talk and so was free to concentrate on listening to others'. One talk gave me useful input on revising a book in a related field for a second edition as I'm currently doing. Other input came from conversations at meals. I met some young people for the first time and got reacquainted with others I had not seen very often. I am happy in my job and not concerned with job prospects, and currently do not have postdocs or Ph. D. students. Our hiring season will be next spring and summer, so I don't know yet whether there will be an impact. Certainly some young people gave talks that impressed me very well. I think the workshop had a very positive impact on the area (high dimensional probability) by indicating which sub-areas are currently making good progress and which others may not be.

I work on applications of Fourier transform to different areas of mathematics. At this workshop I was looking for problems in probability that are related to Fourier analysis. I found several such problems, where I may be able to contribute.

The meeting on high dimensional probability was very attractive. It featured a broad program that included papers on random matrix theory, empirical processes, small deviation probabilities, and a number of other areas that involve interesting directions in probability. When I leave a conference as good as this one I have lots of new energy and ideas. Of course, many of those ideas do not develop immediately, but they certainly provide a template for future investigations.

Mathematics, University of Wisconsin-Madison

The quality of talks was very high and I learned many useful things, as well as got useful information about other colleagues' works not presented in the talks. There was also a very meaningful feedback on my own talk. I appreciated that very much. Some new interesting young people whom I would not meet otherwise were present there. There was also an occasion to push forward some ongoing projects that we had started (with other participants) before the conference.

Mathematics and Mechanics, St-Petersburg State University

The workshop was fantastic. I met a lot of people , whom I wouldn't have encountered elsewhere. I have work for two years !!! Great ;-)

Thank you so much for the organizers for including me. I am a prof at York University. I have worked on other things with Toni Pitassi, Russell Impagliazzo and a few others at this conference, but Proof Complexity has not really been my area. For years, I have been wanting to be able to catch up and learn all about this fine field. At the last minute someone was not able to go and I stepped in. It was a wonderful opportunity. I learned so much. Brilliant people. Brilliant talks. And expect to work more in the area with these people.

The first item is true in all details listed. I learned some new results and got valuable recommendations on what old results I still have to learn. I learned a recently found solution to a problem I have been working on. I made scientific progress during discussions with another participant in some ongoing work started before the workshop. With yet another participant, whom I never met before, we agreed to do some joint work.Two more participants gave me valuable hints on how to proceed with some current work. To summarize, for me this workshop has been scientifically very fruitful, in fact, it establishes some kind of record in this respect.

This is a very quick and spontaneous response, since I have returned back to an impressive backlog at KTH Royal Institute of Technology and am currently rather swamped. Regardless of this, however, I just wanted to let you know that this is very possibly the best workshop I have ever attended. And I spoke to several other participants who felt the same. Proof complexity is an exciting field, that touches on the very deepest open questions in theoretical computer science, but also has close connections to applications (via so-called SAT solving). My personal impression is that the field has been struggling a bit in the last decade, but during this workshop I heard about several new results that are exciting news of progress. The workshop provided invaluable opportunities to meet colleagues and initiate new research, as well as to follow up on ongoing projects. Personally I started two new research projects as a result of this workshop and I hope that interesting things will come out of them (in one we already had some preliminary results while in Banff). Also, it was very valuable to be able to meet and discuss with some of the giants of the field in the relaxed informal atmosphere of the BIRS lounge, and to ask their opinion and advice on various questions. And last but not least, the very venue itself, with its breathtaking beauty, was amazing. Some of the best research discussions I had during the week was when hiking to the Hoodoos and during our outing to Lake Louise. I can only fervently wish that I will be able to visit BIRS soon again...

Thank you very much for this opportunity. This is the area in which I was very active before, but not lately, and this trip was really really helpful to me to get reconnected. I in fact even composed a short list of selected problems asked at the workshop for the benefit of our students (and everyone interested) and it is likely that I will start new research project(s) with other participants.

I had a great time at the workshop, making contact with old friends and learning of new ideas in the area of proof complexity in the wonderful and relaxing atmosphere of the Banff centre. The invitation also prompted me to produce a talk, which I presented. The comments from other participants, particularly Paul Beame, were very useful to me, and led me to correct a serious error in my research -- fortunately not fatal to the main result. Many thanks to BIRS and to the organizers for a great workshop!

The meeting in honour of Robert Moody's upcoming 70th birthday and his contribution to the field of Aperiodic Order was not only very successful, it also came at the right time: it predated the Nobel Price to Danny Shechtman in Chemistry for the discovery of quasicrystals by a few days !! The mathematical activities in the field of Aperiodic Order were triggered by Shechtman's discovery, and the meeting showed how stimulating this has been over the past years. The interaction between the participants was outstanding, and showed the advantage of a relatively young field -- lots of things still to discover. Also, the possibility to stay one day longer was used by a number of people, and proved to be very productive -- sometimes one extra day can help a lot !!

Faculty of Mathematics, University of Bielefeld

The week has been absolutely fantastic - we had lots of excellent talks and many useful informal discussions. Thank you in particular for allowing me to stay for an additional night - the extra day proved very fruitful, as, on a collaborative project with two of the other participants, we managed to understand and solve a problem on Saturday morning which we had been stuck with for a while. I am sure that this will eventually lead to a joint publication which would presumably not have been produced (or at least not until much later) without the workshop and the stimulating atmosphere at BIRS.

The workshop was a very good opportunity for me to meet the world-wide experts in the field to discuss the scientific problems related to aperiodic order. I learned a lot from the comments concerning my presentation at the workshop. It was also inspiring to see the state of the art of research in the different aspects of almost periodic order. I had a number of discussions, which gave me new insight into my own ongoing research. I also continued an ongoing collaboration during the workshop -- direct discussion is much more effective than exchange of notes. It was also interesting learn about a non-intersecting lattice path problem -- this was not in the focus of the workshop, but worthwile for me, since a student of mine has currently worked on a similar problem and might be interested in contacting the speaker.

Department of Mathematics, University of Erlangen-Nuremberg

The meeting was of direct help for my research, in three ways: 1) I got a lot of helpful feedback on the project I'm working on, and on the preliminary results that I gave a talk about. 2) I got to spend time with my collaborator Natalie Frank to plan our next steps, and 3) I learned about other problems out there. In particular, a comment that Jacek Miekicz (sp?) made in his talk let to a bunch of discussions between Jean-Marc Gambaudo and me that will probably result in a paper on the stability of quasicrystals. That's not even counting the indirect help that a conference like this can give. Your brain just works faster, and better, when in the company of the world experts in the field. I left with a much better understanding of the whole field, and not just my corner of it, than I came in with.

Outstanding location and outstanding workshop. All in all, a great place for such meetings.

We would like to thank you for giving us the opportunity to have the workshop at Banff. It was a very successful workshop, attended by 41 participants from around the world. There were 38 research talks, surveying the frontier of stochastic analysis. Participants had engaged in stimulating discussions and scientific exchanges. We also took the opportunity to do some excursions last Wednesday afternoon. The staff members at BIRS are very friendly and helpful. We hope to return to BIRS in near future.

Mathematics, University of Washington

This was a very high-level conference on stochastic analysis, broadly interpreted. The roster of the speakers was selected carefully; the talks were terrific; and the environment was truly conducive to doing quality mathematics research. The conference was attended well, from the beginning to the end of the conference. This was an extremely positive scientific experience.

Mathematics, University of Utah

I really enjoyed the workshop and my stay at BIRS. BIRS did a wonderful job hosting the workshop. I am looking forward to my next visit at BIRS.

1. The participation in the BIRS workshop impacts my current research. 2. The workshop affects my job prospects. 3. The workshop has other impacts on my favorite scientific discipline.

School of Mathematical Sciences, Nankai University

The workshop introduced me to several new contacts whose work is very relevant to my field but whom I would not have otherwise met do to the traditional departmental disciplinary boundaries that divide us. Similarly many of the presentations I found particularly interesting and would not have seen at the other conferences I attend during the year. I took away several methods which I hope to apply to my own research. One of these statistical methods I hope to discuss further with a colleague I met at the meeting and hopefully it can grow into a more substantial collaboration.

Chemistry, Harvard University

This workshop was very useful for raising awareness of potential collaborations with other researchers in the field. I made tentative plans for three such collaborations, and I'm excited to see how they develop.

The workshop was excellent, with a dynamic group of scientists at the top of the field. There was plenty of time for discussion and the selection of talks was fantastic. I came out of the workshop with several new ideas and potential collaborators.

School of Engineering, University of Vermont

It was one of the best workshops I have ever participated in. It certainly has favorably impacted and will continue to impact my research. It allowed me to get a general view of the discipline, learning new things that are relatively far from my research topic and also meeting people and learning lots of things in specialized topics. It certainly has fostered a collaboration, that was barely in progress before the workshop, with one of the participants of the symposium. But it will also allow me to create new connections and collaborations with other participants. It has greatly contributed to get new motivations for my work. I think the workshop had the right combination of: i) exceptional people, ii) researchers from my generation and iii) lots of discussion and questions during the talks. I am definitely grateful to BIRS for inviting me to such an exceptional workshop.

It was a great meeting !! not only in the strict technical aspects, but also on the open and collaborative efforts most of the participants did to 'translate' their expertise to others, which certainly encouraged the 'cross-pollination' of ideas. It profoundly affected my views on several topics that will most certainly imprint on my research activities. My deepest congratulations to the organizers.

Departamento de Quimica Biologica, Universidad de Buenos Aires

It was a great meeting. I got to chat with many colleagues, and talked about future collaborations with two of them. The informal talks helped me put my own research in perspective and think about it in different ways.

Our workshop was an enormous success, and I want to thank you and BIRS very much for providing the perfect location and environment for such a stimulating meeting. I personally met with collaborators to make important progress on two ongoing works, and started three projects with new colleagues. Online feedback from our participants suggests that my experience was commonplace among our participants--Many new collaborations were born out of this meeting, and I expect that the effect of this workshop will be seen well into the future.

My participation at the BIRS workshop was indeed quite useful. Since it has only been a few months since the workshop, the most tangible research that I can point to is a recent paper "Bases for cluster algebras from surfaces" with Ralf Schiffler and Lauren Williams. Having time at Banff to discuss some finishing touches with my collaborators, as well as discuss questions that arose about related results with the other experts attending the workshop was quite useful. Several new contacts were also beneficial, including Demonet, Early, Muller, Plamondon, Tumarkin, among others. I had heard about the work of several of my new contacts (and in some cases been at the same conferences as them before) but this was the first opportunity to have long conversations with them about their research, which were quite enlightening to us both. I am now in the process of pursuing some of the references and ideas that I learned about while at BIRS (both through lectures and discussions around the dining hall). Some of these projects include looking further at atomic bases, as discussed with Schiffler, Thomas, and Williams; investigating more connections to character varieties, as discussed with Muller; and studying (generalized cluster categories and their relation to surfaces, as discussed with Brustle, Keller, Plamondon, and Todorov.

School of Mathematics, University of Minnesota

I discussed with another participant, Leclerc, on his recent new preprint with Hernandez. It gives me a fresh insight on my old result on graded quiver varieties. I have talked with Schroer on my student who will defend Ph.D soon, and plan to visit Bonn. He told me that he welcome my student.

A feature of this workshop is the opportunity provided for interactions between the participants. Workshop organizers have facilitated round-table sessions in which questions and answers were shared, and lively discussions were encouraged. Invited participants are from diverse interdisciplinary background and top in their field. Such a combination of ideas and perspectives have been beneficial to all attendees. The workshop presentations, discussion in the round-table sessions, and potential collaborations amongst participants have created the opportunity for meaningful progress in the field of energy and environment modeling and simulation.

Chemical & Petroleum Engineering, University of Calgary

I believe this BIRS visit has indeed helped me, in letting me show some of my results to important contemporary applied mathematicians, and in making new or keeping strong contacts. As concerns of concrete, present and future effects, other that those stated, it is still early to make an assessment, but, as I said, I believe strongly BIRS visit has provided me with a strong forwarding jump for my mathematical career. If at least one good collaboration starts out of this, and this in turn results in a good scientific paper, then I think my expectations would have been more than exceeded, beyond the positive effects I feel now. At any rate, BIRS environment is surely inspiring, and I for one will tell my colleagues to seize the opportunity to assist to BIRS, if they have the chance. I would like to thank you and of course the organizer, Zhangxin John Chen, who will be with us soon, at the mexican petroleum institute.

Thank you very much for your arranging me at Banff. It is a beautiful place. I shall remember this trip.

Attending this Workshop of Modelling and Simulation was really exciting, not only for the academic experience but also for enjoying the beauty of nature here. It was a very spiritual experience. I really felt I could be one with Nature for a while. I could contact people in order to (potentially) publish papers, I got new ideas for my own research,I could learn other perspectives of my own field of reasearch,etc. Definitly it was an amazing experience in all senses.

Departamento de Matematicas, Instituto Tecnologico Autonomo de Mexico (ITAM)

It was a great workshop, in a marvelous and inspiring setting. Fruitful discussions did help me a lot to get new ideas for future work and to get insight in other people's work. The informal atmosphere contributed to better collaboration opportunities.

Department of Mathematics and Computer Science, Eindhoven University of Technology

I met several people whom I had not met before, and in particular learned about work on functions given by images and the special interest in the case where these are Morse functions. I was also able to talk to a participant about persistence homology which enabled me to write a much better review of a research proposal from the European Research Foundation. I was able to spend very useful time with Prof James Damon, also a participant, working on a joint project which we have in progress. This will lead to a research visit by myself to Prof Damon. And of course there is the general interest of the lectures, many of which were really informative and interesting.

I really enjoyed the workshop and met a lot of new colleagues. It was inspiring and refreshing to see different view points on an interesting topic.

The workshop most certainly extended my horizons by getting know a lot of work outside my field (yet relevant to my work!) Hence, I found the workshop immensely valuable.

School of Computing Science, Simon Fraser University

I am most grateful that I had the opportunity to participate in this BIRS workshop on Geometry for Anatomy. It has been really great: a lot of excellent talks and very serious discussions, a good mix of people from overlapping but not identical areas. I left this workshop with fresh ideas and also with a specific topic for cooperation with one of the participants. I assume that BIRS has been modeled a bit like Oberwolfach in Germany. I must say that you did a great job in achieving this (of course, the scenery in Banff is a lot nicer than in the German Blackforest .... ).

In the workshop we gathered knowledge of different fields where the queuing theory can be applied and got to know about a lot of queuing models and other stochastic modeling methods. It will for sure help me in my future studies.

Personally, I learned quite a lot at the CanQueue workshop. In particular, I got a good introduction to the application of queueing in health, and I learned about queueing in radio networks. Both are applications of mathematics to urgent problems of society. The meetings were all well attended, and a significant part of the meetings were used for questions and discussions. In conclusion, I thank BIRS for its support, and I hope you continue your valuable services in the future.

I received useful feedback and suggestions on two of my current research projects. My doctoral students made contacts with their peers and with top queuing theory researchers. The process of forming a Special Interest Group (SIG) on queuing theory and applications within the Canadian Operational Research Society (CORS) started during the workshop.

It was our pleasure to visit BIRS. BIRS is an outstanding center for researchers in order to get together and have scientific discussions. Once again it was an excellent experience for all of participants to be in BIRS as indicated to me. The group of people working with you in both Vancouver, Wynne and Brenda, and in the Station, Kameko and Caroline, did an excellent job for us and we are really appreciate their work.. They manage everything in a high level, nicely. We, as Canadian researcher, should be proud to have a such facilities and I hope in the near future we could visit BIRS for more research activities. Once again, I would like to thank you and your people for helping us to have Canqueue11 in a very nice environment.

The workshop helped me a lot. I entered this area 4 months ago and what I am working on is a specified 3-D random walk. I met Dr. Li here and her suggestions about this model are really helpful. And Barbara Margolius's work is interesting for me, maybe I would like to have a try to work on it. Besides, It is the first time for me to see some real applications of queueing theory which are very interesting. Also Dr.Grassmann and Dr.Tavakoli's question about the effects of numerical methods is thought-provoking. And Dr. Zhang gave me some career guide from the prospect of an applicator.

BIRS is a wonderful place to work with people that have common interests. The atmosphere, the faciities, and the great surrounding are very inspiring. With the workshop I had the opportunity to meet people whose work I knew very well and discussed several ideas.

I have found the workshop "Crossing Numbers Turn Useful" very stimulating. We had plenty of opportunities to work together on various problems, which we certainly used. In particular, in addition to continue already existing projects/collaborations I have started a collaboration on new project that was motivated by crossing numbers but which is a different area. I feel that we have made tremendous progress and hope to be able to return to Banff for similar programs.

The workshop was very nice. The small number of participants (20) gave it a friendly atmosphere. We have attacked several problems outlined at the problem sessions, and at the end of the workshop some serious success has been reported. Personally, I am already preparing a manuscript with Zdenek Dvorak about computability of the average crossing number, a problem asked at the meeting by B. Richter and G. Salazar. I also took opportunity to work with Dvorak and Hlineny on our long time involvement towards describing structure of crossing critical graphs. Nice partial success was achieved.

This has been really the perfect workshop. It has achieved the perfect balance in putting together a group with different backgrounds but definitely with common interests. As a result, the work these days has been really enriching, opening new approaches to important classical problems and new insights to the relation between different, but neighboring fields.

I think this workshop inspired me to consider other directions towards the resolution of the central problem in Cosmology. Furthermore, various issues that were somewhat obscure to me before this workshop became much more clear. From this perspective it did impact my current research and I believe the new results will follow shortly.

BIRS provided an excellent opportunity for communication and collaboration within the crossing number community through this workshop. The facilities are excellent and the location is beautiful. Thank you for supporting our workshop! With Balogh and Czabarka we checked that certain type of arguments cannot prove the Albertson Conjecture - but still proved something positive. We also formulated a new conjecture: the crossing number of the complete on n vertices is a concave up function. The truth of this conjecture would effect the truth of the Albertson Conjecture. As the these crossing numbers of complete graphs are asymptotic to (an unknown) constant times n^4, this conjecture is true unless the crossing number show a very erratic behaviour, which is certainly not present for the first few known values. With Bokal and Czabarka, we collaborate on a topic on how to optimize lower bounds for crossing numbers that can be bigger on a subgraph than on the whole graph. Although we started this project earlier, meeting in person moved the project ahead.

The workshop was a great opportunity to discuss information theory problems in depth and in a wonderful setting. I think a more relaxed program would also be fine since the main point is for people to make the time and think deeply. The BIRS environment is truly inspiring creativity.

I got new results that I had studied and also relations with another areas.

The workshop has been a wonderful experience for me. The talks provided a comprehensive and inspiring picture of the cutting edge research in the field. Through conversations with the participants I discovered new approaches to develop a promising direction of research which will involve quantum versions of vertex algebras.

School of Mathematics and Statistics, University of Sydney

The conference was great. Everything was right - the organization, the participants, the timing, etc. It was my 4th time (I think) at BIRS and I would come again anytime. I have surely learned many things and even started a couple of new projects. It is too early to say how they will go, but it is certainly a very interesting twist...

The workshop was wonderful with lots of interactions with experts on quantum groups.

Mathematics, University of California, Davis

The meeting was superb. Aside from the stimulating formal program, I was able to meet some colleagues whose work I was unaware of and found most exciting. I expect some of those interactions will lead to real collaborations. I intend to invite at least 2 of the participants to visit our center during the next year. It also gave me a chance to reinvigorate previous relationships.

The workshop was a little outside my area of expertise, so I did not know exactly what to expect. It was fabulous! I came away inspired and enthused, with many new ideas and hopefully future collaborations. The group size was perfect, there was a lot of useful discussion and I particularly enjoyed that even disagreement was constructive. The organisers deserve an enormous amount of credit for bringing together this group and inspiring this atmosphere of collegiality.

Again, a terrific meeting in Banff. The BIRS is the best venue I have been to for a scientific meeting. The organizers put together an outstanding program.

The organizers assembled an ideally balanced group of junior/senior, female/male and physical-mathematical/biological scientists for this stimulating meeting. Everything ran on time and allowed for lots of stimulating discussions.

Molecular Cellular and Developmental Biology, Yale University

This meeting was a tremendous success and multiple participants told me this was perhaps the best scientific meeting they had ever attended. The facilities, support, participants and format of the workshop were obviously significant factors, and the fact that we had absolutely perfect weather all week certainly helped as well. Brenda was also a really great asset and helped in many aspects of the planning, organization and operation of the workshop. I expressed my personal thanks to her, but I wanted you to know how valuable she was in making this a success (I'm sure you knew that already). As for BIRS, this is a very unique scientific organization with no equal. We feel privileged to have been selected, and hope that the outcomes, collaborations, and breakthroughs resulting from this meeting will help ensure the success of BIRS in the future.

My participation in the BIRS workshop had a positive impact on my work, primarily because of the comments I received from colleagues after presenting a recent result. This lead to a discussion of a physical phenomenon directly connected with my mathematical result that I had previously been unaware of.

Thanks a lot for running such a terrific program. It helped a lot in strengthening the communication between analytical and experimental studies of pattern formations, and sharing the new developments in this field. I personally like it very much because I was able to meet many authors of the references I cited, it was great to talk to them and have some discussions. Besides, the stay in BIRS was very nice, and the manager was very helpful and hospitable, I had a wonderful time at the workshop. Thank you very much.

I very much enjoyed this BIRS workshop, which was particularly interesting, not only because of the mixture theory, modeling, and experiments. On short time, I could advance on my current work (theoretical), but could learn a lot from the talks on modeling and experiments. Meeting people from so different areas, and having the possibility to discuss with them was a great experience. Moreover, the environment at BIRS contributed a lot in the success of this workshop. It is a great place and thank you to you all for making this possible!

Departement de Mathematiques, Universite de Franche-Comte

Several of the talks were very inspiring. Scott McCalla (one of my former students) and I were fascinated by Kondo's talk on pattern formation in zebra fish and plan to work on a mathematical explanation of his findings using agent-based models. Furthermore, I started another collaboration with Arnd Scheel. I learned more about various areas, such as matched asymptotic expansions, than I had hoped for. The talks also helped me to prioritize some of my projects. Overall, it was a very helpful and inspiring experience.

The workshop was really a great occasion for all participants, who expressed to the organizers their happiness to meet, work and stay in such a wonderful place as the BIRS. The BIRS organization and assistance were simply perfect!

It's a great experience for me in this workshop. The talks were stimulation, and more important, there were so many interesting discussions between various groups of the participants. From my part, during the workshop, C.S. Lin and I made some further progress in our on-going project on local isometric embeddings of Lagrangian surfaces; Colesanti, Salani, and I initiated some new ideas regarding the establishment of Alexanderov-Fenchel type inequality for quermassintegrals on non-convex domains. It's our hope this will lead to some breakthrough of the problem in a near future. I also had some inspiring discussions with Cabre, Ni and others related to level-set convexity of solutions to nonlinear PDEs. The setting and the organization of BIRS is superb and unique for the inspiration of mathematical ideas.

Mathematics and Statistics, McGill University

It was a great meeting, I was able to go on works and discussions with four colleagues and friends, making significant progress in two cases and initiate new collaborations with two other young Italian colleagues The working atmosphere was quite good.

Universite de Nancy, Institut Elie Cartan (France)

The workshop highly impacted my current research. It helped pushing forward an important research project and led to its further improvement. I met a number of new and very interesting people that I had not met before. I profited immensely from the presentation of their work.

The workshop was very fruitful and completely satisfactory to me. It gave me the opportunity to establish new contacts and discuss with many experts in my discipline; some new collaboration could easily arise from this experience. I want to thank all the staff of the Banff International Research Station.

This workshop was extremely beneficial to me academically. The chance to network with such high-level researchers and to share my work with them, in such a beautiful and energizing part of the world, was unparalleled. I will certainly recommend BIRS to my colleagues when they are looking for places to hold a conference.

Mathematics, Texas A&M University

First I would like to thank BIRS for the support to attend the workshop. The workshop is quite special for me. There are at least half of the speakers are biologists.They show us their biological viewpoints of Spatial Ecology.It help us mathematicians to construct different type of mathematical models. In the workshop I discussed with some people and learn that we have some overlaps in our work. It is good to know other's people work related to your work. Also I learn some progress made in the principal eigenvalues. Mathematicians and biologists think in different ways. I hope in the near future I shall have opportunity to collaborate with the biologists I met in the workshop.

I have participated recently at the workshop Emerging Challenges at the Interface of Mathematics, Environmental Science and Spatial Eco. Although during my career I attended several conferences and workshops, this one was really unique among them. First of all, there were the most outstanding scientists in the field of theoretical spatial ecology I can think about. Second, the workshop organization was really excellent. The workshop brought together people from different fields (i.e., pde, game theory, real applications), that would otherwise probably never met. And I'm pretty sure that this diversity will lead to new results and publications. For example, as I'm working mostly on game theory, this workshop was a unique opportunity for me to learn how partial differential equations are used to solve a similar problem. Indeed, I started some new collaboration during the workshop. Overall, I have to say that my experience from this workshop is very positive, I started some new collaborations, and learnt things I would have never learnt otherwise. I thank B.I.R.S. for this unique opportunity.

Theoretical Ecology, Biological Research Center

The participation in the BIRS workshop will likely foster some new collaborations, e.g., with Cressman and Krivan on the theory of ideal free distribution, and I hope to report papers in near future.

The workshop renewed my excitement about the research area. I met a number of people whose papers I had read, and I had the chance to talk to them directly. I have a number of new contacts that I would not have had otherwise. The group discussions were very stimulating, and their content will be a source of inspiration for the next while. The only reason that I did not get new research projects out of this meeting is that I already have too many projects going, and I deliberately decided not to start anything new. Otherwise, there would have been many opportunities.

I enjoyed the workshop very much and expect that it will result in a number of continuing collaborations. The place and the facilities are incredibly nice!

This workshop was one of the most stimulating meetings I have attended in years. Aside from learning about many new research directions, I received valuable feedback on my own research project which will result in an improved forthcoming paper.

Mathematics & Statistics, Arizona State University

I indeed opened some collaborations with some participants in the field of spatial and evolutionary ecology modeling. I got quite a few interesting ideas and learned a lot from the workshop.

Mathematical and Statistical Sciences, University of Alberta

I feel my visit to BIRS was very beneficial to my current research. I would like to thank the organizers and the staffs of BIRS very much for the very stimulating workshop and hospitality extended to me during my stay there.

Department of Mathematics, Graduate School of Science, Osaka City University

This was a very informative workshop and I must say that I learned a lot from other participants, including computer scientists and mathematicians. Definitely I'll try to use the software Prover9 and its future renovations to solve problems in my research and teaching. The atmosphere was informal and very friendly. Everybody is ready to help and share with other people. The ac commendation and food service was excellent. Looking forward to attending another conference or workshop in Banff Center in the nearest future.

Unit 5: Math, Stats, and Physics, University of British Columbia, Okanagan

Through my participation at the BIRS workshop, I made several new contacts and learned quite a lot. I began a collaborative project with Yair Glasner (whom I just met for the first time) and Miklos Abert on generic graphings and invariant random subgroups. I also learned a lot from Anders Karlsson (whom I met for only the second time) about his work on random walks and possible applications to a current research project of my own. Also I spoke frequently with Russell Lyons and Vadim Kaimanovich, learning about the current work which impacts my own very much. I also spoke with Yuval Peres on reverse martingales - which might impact some of my work on pointwise ergodic theorems. All in all, it was a very enjoyable and fruitful conference.

I am definitely very happy that I participated to this workshop: it was very helpful to meet people interested in my same topic. Moreover I had the possibility to exchange some ideas about mathematics with some of the participants. It is even possible that some collaborations will arise after this visit, but it is still too early to say. Since I am still a PhD student, this workshop was very helpful to get more involved in the topic, and to think further in the perspective also of a possible postdoc. During this workshop I have learned many new things, and got more information about the ones I knew. I hope there will be more workshops like this one!

Department of Mathematical Structure Theory, Graz University of Technology

This week was very fruitful for me. I made some new contacts, that gave me some feedback on the research I presented. I had several stimulating discussions, where some of my ideas was potentially useful for others, in for me unexpected way. A couple of the talks directly lead to a research project, that I want to work on the coming months. It concerns trying to modify the methods in a recent paper of mine to problems of another type. I will the two scientists again in the fall at MSRI and my hope is to be able to report on progress in this direction then. At present time, there seems to be no effect on jobs for me or my students or postdocs, except for the general network building. People were very excited about the workshop. Many said that all talks were very interesting and stimulating. I agree. So the impact is/will be significant on the subject. It was a very well chosen topic(s), quite of current interest and activity.

There were great talks and I met new people. It is too soon to say there will be new collaborations, but that is possible.

The workshop was a great opportunity to me to be in contact with a community slightly different from that I used to be in permanent contact. The presence of certain people has been crucial for instance to solve some problem concerning my most recent publications.

Mathematics, Universidad de Santiago de Chile

The Alberta Number Theory Workshop was indeed a success. There were several stimulating talks, and the large proportion of graduate students (and I believe one undergraduate!) benefited from being exposed to several interesting avenues of advancement.

The Alberta Number Theory Days conference is a great opportunity for us, number theorists in Alberta, to maintain a tight scientific bond among us. The workshop was very good in both the scientific and human aspect: - the quality of talks was very good, with new and interesting results. It was an opportunity to discover the research of people who recently moved in Alberta, such as postdocs. Also the senior professors gave very good lectures that were accessible to the younger attendance, such as graduate students. I am sure that they got a lot from these talks. - the facilities at BIRS are very good and the size of the conference is perfect to allow interaction with other researchers, even outside my area of expertise. This may not have happened in another type of workshop. I personnaly got to learn about new results and get feedback about my work, which gives me new perspectives for my work.

Mathematics and Computer Science, University of Lethbridge

The scientific program for the workshop was excellent and varied greatly, even within the field of number theory. Although the program won't impact my current research, the workshop did give me several ideas for future projects and allowed me the opportunity to collaborate with my peers on ongoing projects.

Although the topics itself was above the level of my studies I think the whole conference was interesting for me because some of the subjects may be related to my future area of researching. So that is my pleasure to attend such a conference and I hope I will have the opportunity to attend such a conference in the future!

I enjoyed the workshop very much. The following comments are symptomatic: * Many new and interesting aspects of number theory have been presented. * Two collaborators of mine were attending the workshop and were giving talks. * I obtained new ideas and started new projects with the collaborators. * The friendly atmosphere of the workshop was very important for creativity. * I obtained several new ideas for research topics of my Ph.D. students in Germany.

Mathematics, Carl von Ossietzky Universitat Oldenburg

I have enjoyed this conference enormously, and I am grateful to the organizers for the opportunity to give a talk to such a distinguished audience. It was quite satisfying to see triangulated categories bring together researchers from such varied subjects, and I had a great number of stimulating discussions with several of them. For instance, I have started right then a collaboration with Goncalo Tabuada which has already produced a preprint ("Morita homotopy theory of C*-categories"). At least one other collaboration started then is still in incubation.

The conference was wonderful, and I felt like I came away with several new ideas for research projects. Some new results did originate during the conference, from discussions with other participants.

I belonged to the smallest group of the participants, algebraic geometers. But other participants were very friendly, and I got some familiarity to the subject, the category theory. Of course the participation to a conference did not have an immediate impact, but I believe that the new connections made at the conference will have a long term impact.

Graduate School of Mathematical Sciences, The University of Tokyo

The conference was a great success. I learned a lot about triangulated categories in different domains of application, esp. in algebraic topology, an area which will become increasingly important in my future research. I also made interesting new contacts, and had the opportunity to discuss with experts some ideas related to the work I presented at the conference. This will have a very positive impact on my research in the very near future, and is also likely to result in new collaborations.

Department of Mathematics and Informatics, Universiteit Antwerpen

This workshop brought decisive new ideas for several projects I have been working on. I view triangulated categories as a link between my field, noncommutative geometry, and homotopy theory and representation theory. I find it very stimulating to meet experts in these other fields because o their complementary interests. The lecture by Strickland allowed me to connect previous work of mine on bivariant K-theory for certain diagrams of C*-algebras to May's axioms for tensor triangulated categories. This showed the way for a joint project with Tabuada to understand these axioms. I got several representation theorists interested in the hereditary exact categories that I constructed in this work on diagrams of C*-algebras, which may lead to future collaboration. I happened to meet Ferdinando Muro who knows a lot about strictification of symmetric monoidal categories, which is exactly what I needed to understand the question of uniqueness of differential extensions of cohomology theories.

The subject of the workshop was a very interesting one. Most speakers talked about their latest discoveries. I got much feedback after my talk. The organizers managed to gather an interesting group of people. I am happy because I managed to attract the interest of some experts in module theory to open problems in that area that arose in my research on algebraic topology. In discussions with another participant which focuses on differential geometry and analysis, we have come to solve an open question about the uniqueness of differential cohomology theories. I have also met there for the first time to some keynote researched that previously I only knew from references. Overall, I am very satisfied with my participation in the workshop, I do think it will be very influential in the direction that my future research take.

Algebra, Universidad de Sevilla

This is a wonderful workshop. I met several old friends and made some new friends too. Also, it is very high standard scientifically. I presented our recent work and learned many new stuff and the state-of-the-art in the field. I am benefited significantly from attending this workshop.

Department of Mathematics, National University of Singapore

I'm very happy with my participation at the workshop: KAM theory and Geometric Integration. The organisation and the talks were very good and I learned a lot: problems, results, people. I also had time to work with one of my collaborator.

It was a great week at BIRS, and quite an unusual set of people to convene. It was a combination of mathematicians in Hamiltonian dynamical systems and KAM theory, meeting the community concerned with the numerical analysis of Hamiltonian systems with many degrees of freedom (such as the n-body problem). We had several of the big names in symplectic integration techniques, both those who have worked out the theory (such as Ernst Hairer - Geneva) and those who us it in their large scale numerical simulations (such as Carles Simo - Barcelona). We also had several of the most active people in dynamical systems, KAM theory and Arnold diffusion (Rafael de la Llave - University of texas - Austin), Nekhoroshev stability (Dario Bambusi - Milano), and Birkhoff normal forms (Thomas Kappeler - Zurich). I myself learned many things about numerical stability of simulations of the N-body problem. In addition I had an intense time of collaboration with Philippe Guyenne (University of Delaware) having to do with Hamiltonian PDEs, the modulational approximation in the presence of resonances, and the description of a particular physical phenomenon of a `rip' wave train which accompanies and is the signature of a large internal ocean wave. Thanks again for the stimulating environment.

Our workshop was a success in part thank to the organisation of the BIRS. The two communities, theoretical and numerical, have benefited of this unusual mix. This workshop allows me to contact some researcher I never met before.

This workshop was the first that brought together people working on theoretical aspects of KAM theory and numerical analysts interested in geometric integration. I belong to the second group, but I profited a lot from the talks and from discussions with people from the other group. Some ideas and techniques are closer than I thought before the workshop. In my opinion, the workshop was really a great success.

I have enjoyed the workshop immensely and I profited a lot from the discussions with colleagues as well as their feedback to my talk. In addition, the workshop gave me the opportunity to meet for the first time people I always wanted to get to know in person.

This workshop was a very interesting mixture of two different communities, from KAM and geometric numerical integration. I was very happy of that. Every speaker made a real effort to speak to the whole assistance. As a result, the ambiance was very relaxed and offered a lot of opportunities to discussions.

IRMAR, Universite Rennes

I appreciated very much that specialists from different communities (dynamical systems and numerical analysis) were at the workshop. This created a very inspiring atmosphere, and I got new ideas to treat an old problem.

It has been one of the better experience I ever had on workshops, especially for the scheduled plan, which included only 4/5 long talks a day, starting not too late in the morning (8:30 a.m.) and leaving the after lunch time for discussions or personal businesses. About the scientific point of view: I had the opportunity to discuss with some young researchers about some topics on PDE I'm interested in, but with respect to which my knowledge is quite poor. These connections are expected to be useful in the next future for possible visits and even collaborations. Furthermore, I took the chance to start thinking about a new result on my favorite topic. The level of most of the talks have been pretty high, in spite of the differences among the communities. The experiment of mixing people working on numerics and on more abstract topics have been however successful, I think.

Mathematics , University of Milan

I really enjoyed attending the meeting on KAM theory and Geometric Integration. Thank you for making this possible. I take this to congratulate you. The staff has an impressive efficiency and everything is prepared to make the stay pleasant and fruitful. My best wishes for the future of this magnificent centre.

The BIRS workshop gave me new contacts I wouldn't have had otherwise and also fresh insight on a field of study I was not so familiar with.

I found the week in Banff very helpful for my research program. Although I benefited from all the talks there were three which were of particular interest to me: (a) talks of Funaki and Nishigawa: In these talks the speakers discussed their work on hydrodynamic limits. I learned that so called Glauber dynamics leads to second order equations and Kawasaki dynamics to fourth order. These fourth order equations are of Cahn-Hilliard type. I have been studying Cahn-Hilliard equations for several years now in the context of understanding the phenomenon of coarsening, so it was very interesting for me that these equations can be derived from a microscopic model. I think this may have some relevance for my research in the future. (b) talk of Felix Otto: This talk was very close to what I have been working hard on for the past year or so. It is a kind of parallel development to what I have been doing. Otto has been studying rates of convergence in homogenization, while I have been working on the asymptotics of averaged Green's functions for solutions of PDE with random coefficients. Otto has stronger results in his situation, so I am looking forward to applying the new methods he has developed to the problems I have been working on. Apart from professional enrichment, the week in Banff was thoroughly enjoyable for me. The accommodation and food were excellent, and the splendid natural environment absolutely wonderful. I am very glad I had the opportunity to attend the workshop.

The workshop was very stimulating because the speakers of the talks belonged to three different areas of Mathematics: Analysis, Probability and Math Physics; and yet we were all studying similar problems. Of course for me it was a good occasion to present to an audience of experts my recent results and, most importantly, my methods, which are slightly different from the one used my the majority of scholars in the field. Besides, during the long pauses between the morning and the afternoon sections, and even during an afternoon hike in the mountains, discussions with some of the participants gave me new points of view about a certain class of models that I am studying currently: hopefully this will lead to some progress.

The participation at this workshop did had a very good impact to my research. I particular I started two new collaborations with participants at the workshop, and had many stimulating discussions. I did not gave a talk myself, since I do not have recent results on the specific topic of the conference.

Mathematics, CEREMADE - UniversitÃ© Paris Dauphine

I think we owe BIRS a great thank you note more than anything. As you know, our main goal with this meeting was to discuss technical problems related to our network, aiming at strengthening collaboration and identifying further avenues for joint work. I am sure I speak for all when I say BIRS provided us with the ideal setting in which to have a focused and productive meeting. All the feedback I got, and I did get lots of it, pointed to people finding their visit extremely worth their time. I know our researchers will look back at our BIN@Banff meeting as a highlight of our network. Most attendees had their first visit this past weekend, while some were coming back after several years. The consensus, however, is that BIRS is a truly outstanding facility and a tremendous resource. We will certainly not hesitate in coming back should another opportunity arise. I would also like to thank BIRS and Caroline for your hospitality.

I had a great time in Banff. I just finished putting my notes in order and wrote down a whole page of insights and action items. It was a very stimulating and fun event!

My participation in the BIRS workshop on Data Analytics was very helpful to my research. It provided a unique opportunity to interact with colleagues in our research network and to develop and explore new collaborations.

Computer Science, University of Toronto

The workshop offered a wonderful opportunity for the academic participants to interact with each other and with the industrial partners. I expect two and possibly three new collaborations to arise from contacts made at the workshop.

The research workshop helped me understand new trends in Data Management and Business Intelligence; in terms of Real-time and Live Business Intelligence, Social Data Analysis; and their associated collaborations in research in the NSERC BIN network. Also, the workshop made me make new contacts of researchers from different Universities; since the BIN network comprises of different researchers.

SCHOOL OF INFORMATION TECHNOLOGY AND ENGINEERING (SITE), University of Ottawa

It was great. I think that I will start a new long term collaboration based on it.

The workshop was great and I made valuable contacts.

School of IT and Engineering, University of Ottawa

The BIRS workshop greatly impacted my research. In general, over the past year I have wanted to begin a successful collaborative mathematical project in algebraic combinatorics, with an aim of broadening the scope of my active research beyond the immediate sphere of my thesis. Geographical and financial constraints make forging such collaborations difficult, and I am incredibly indebted to the organizers for helping to make this professional goal a reality during the BIRS workshop. In particular, there was a new project that I was interested in working on, for which I did not feel as though I was individually equipped with the requisite background. I proposed this problem to my designated research group, we generated a conjecture which would solve the problem, and we currently have a working draft of a joint paper. Of the four other group members, three of the four are individuals with whom I likely would not have had a chance to collaborate otherwise, and whose energy and expertise were vital to the movement of the project. My group members will certainly remain important contacts for me, and without the workshop several of these professional relationships would not have been made. Moreover, given more time at the workshop, I am confident that one or two additional collaborations might have begun, both with people in and outside of my designated working group.

Mathematics & Statistics, Williams College

On behalf of all 42 participants of the Algebraic Combinatorixx Workshop, I would like to thank you and BIRS for inviting us to hold this meeting in such a spectacular venue. The workshop achieved its goals of introducing participants to recent developments in areas of active research and of fostering much collaboration. BIRS was an ideal location to make this happen. The response to the workshop has been quite overwhelming.

The participation in the workshop was an amazing experience. The quality of the talks was exceptional, and the discussion between talks was very lively; I met many mathematicians (in particular younger ones) whom I hadn't known before. The 'research in teams' initiated by the organizers will probably lead to a joint paper with members of the team; it was a fruitful discussion on quasisymmetric analogs of Schur P-functions which both are among my current research interests (apart from the organizer Steph van Willigenburg I had not met any other member of the team before). A talk of one of the principal speakers (Anne Schilling) on the rather new topic of k-Schur functions together with direct exchange on her data on k-Schur functions already led to a conjecture on the determinants of the corresponding tables and a refined one on the invariants; this is closely related to my own work on character tables of the symmetric groups. We have exchanged emails after the meeting and will keep in touch on these questions. A poster and short presentation by a younger participant (Kelli Talaska) on determinants for special graphs led to an exchange on determinants and invariants for paths in certain quiver algebras, where formulae of a similar structure occurred in work of mine; it is not clear yet what can be learned from this observation. Also, data on the composition poset appearing in work with Steph van Willigenburg and collaborators were discussed also with Georgia Benkart; here, the question is whether the data helps in finding an algebra that is connected with the composition data.

Department of Mathematics and Physics, Leibniz University Hannover

This was, by far, the best conference I have ever been to. Everything was organised as to maximize interactions between (junior and senior) participants. And it worked brilliantly! I have come back with several new research projects with new collaborators. More specifically, I have started a project with Rosa Orellana on the restriction/induction rules for the Partition algebra (and other diagram algebras). This should give a new approach to the longstanding problem of describing the Kronecker product of Schur functions. With my "working group" at the conference (Benkart, Vazirani, Parker, Orellana), we have started investigating possible representation theoretic interpretations of the quasi-Schur functions introduced by van Willigenburg, Mason, Bessenrodt and al. and we plan to continue this work in the coming months. Following my talk at the conference, I have also had very useful discussions with Georgia Benkart, who suggested new directions for my own work, such as investigating the representation theory of the derragement algebra, and the relationship between the decomposition of tensor space for the orthosymplectic super Lie algebra and the Brauer algebra. I would also like to mention another aspect of the conference which (indirectly) influences my research as well. I did not know there were so many women in this field. I usually only meet a few at conferences. And many of them face the same challenge of juggling research and family life. I felt really encouraged hearing about other (more senior) people's stories and sharing experiences.

Centre for Mathematical Science, City University London

This was an extremely valuable conference for me, and I believe for many other participants as well. I was actually a little skeptical of the idea, but I think it worked well for a couple reasons -- a tone was created in which speakers felt comfortable trying to make talks as understandable as possible (rather than feeling like they simply should impress people as much as possible), and I think there was a team spirit created in which people really did try to draw in and help the younger participants both to learn about important areas and to get included in new collaborations.

Participation in the BIRS workshop Algebraic Combinatorixx led to new research ideas, new research collaborations, and meeting new people. This was a fantastic workshop, well scheduled to really take advantage of being at BIRS. We had many interesting talks, but also plenty of time dedicated to small working groups. This workshop had a secondary theme beyond the research topic. It was an all women's workshop and time was set aside for panel discussions and general group discussion of the issues and difficulties facing women in mathematics. I truly appreciate BIRS supporting this additional aspect of the workshop. It is hard to describe the need and positive effect such gatherings have for female mathematicians. Among other things, I was "re-charged" to come home and face the challenges that arose while I was away.

I found this conference to be well-organised with a surprisingly refreshing format. The organisers decided to have more expository talks - from which one learns more anyhow and fewer talks in general in order to put an emphasis on group discussions. My particular group was a good mix of people from different backgrounds and stages in their career. Our group started a project in a area that is new to all of us but for which our common background allowed us to discuss. I learned quite a lot from these discussions as well as from the talks. We hope that a paper (at least one) will result from this collaboration and are in the process of working further on it. This collaboration most likely would not have started up without this conference. Although this workshop did not personally affect my job prospects as I am tenured, it was a valuable opportunity for mentoring as most of the participants were in the early stages of their career. I had some doubts about the all-woman format before attending, but was pleasantly surprised on how the whole thing worked out. I would say that it was one of the most effective workshops that I have attended and the organisers are to be congratulated.

The workshop impacted my current research. In our group, we worked on quasi-symmetric Schur P-functions. We conjectured the formula for that and plan to work on more problems related to quasi-symmetric Schur P-functions. We hope to write a paper together. In this workshop I worked with some professor from Korea. This was the first time I could collaborate a Mathematician from a such far place. The workshop affected my job prospects. The other participants told us that women in Math usually are more productive as age grows.

Mathematics, Drexel University

This workshop was the best of all workshops/conferences I have ever attended. I am so happy I was able to be at BIRS. I have learned a lot of new mathematics and new perspectives on mathematics, as well as found new potential research projects and collaborators that I likely would not have found otherwise. My time in Banff was very rewarding and enjoyable!

I had conversations with many new people that might ultimately lead to research collaborations. For example, Patricia Hersh came to my informal presentation on crystal bases and got an idea on how to apply this to symmetric chain decompositions of the Boolean algebra modulo a cyclic action. As a result of our discussions at the workshop we published the following article:http://arxiv.org/abs/1107.4073. Georgia Benkart had some interesting question regarding the decomposition of tensor products of Demazure characters. Christine Bessenrodt made some interesting observations about the character tables I presented in my talk.

The workshop was incredibly useful for me. I expect 2-3 new collaborations to come out of conversations during the workshop. I found out about some jobs that sounds like especially good fits for me, and got advice on contacts for those. I met quite a few new people, and managed to form better relationships with others I had briefly met before.

Mathematics, University of California-Berkeley

This was the best conference I have ever attended. The mathematics was superb, and I have started (at least) two new collaborative projects as a result. Additionally, the opportunity for panels and other discussions about women's issues in academia/mathematics was very valuable. I hope we can do this again!!!

This was a fantastic workshop. The scholarship was outstanding. The focus on professional development was at an exceptionally high level. The research that I began during that workshop has continued with a dedication that I have never experienced in a research group this large, or from research arising out of an impromptu discussion. The professional contacts that I made and solidified promise to be exceedingly useful, both to my research and career more broadly (mine as well as theirs, I hope). The organizers are to be commended for the time, energy, and thoughtfulness that they put into this conference. I hope that BIRS will support more workshops of this form---I can only imagine the scientific impact if every research area had a group of organizers who could bring together women in their discipline this effectively.

Every time I have the opportunity to attend BIRS I have an outstanding experience. This workshop was no exception. The opportunity to meet a wide range of women algebraic combinatorialists led to my making many new valuable contacts across the globe. Furthermore the breadth of talks and high quality of exposition meant that I cemented a number of concepts and deepened my knowledge of many more. The poster sessions for graduate students helped them to bring their research to the attention of many senior mathematicians, and the panels gave much valuable insight to life in academia for all participants. One of the most amazing aspects of the workshop was the collaboration groups, which brought together researchers of similar interests in groups to discuss open problems. By the end of the workshop at least four papers were originated (my group included), with the amenities that BIRS provides being crucial to the success of these projects: breakout rooms to work in, the library for resources, the lounge for continuing discussions late into the night, the mealtimes for swapping ideas with other groups. As an organizer, I was thrilled to hear from a number of participants that this was the best conference they had *ever* attended, and that BIRS was a fundamental contributor to this.

My participation helped me to strengthen my knowledge on current ongoing research especially in my field which is Functional Analysis, Geometry and Probability, and of course, present a talk on new very recent joint results I had with colleagues. My job is secure and so Birs had no effect on job prospects. The workshop was important and interesting and it will take to digest its significance on my research. I was encouraged to see that my current joint research is interesting to other mathematicians in the workshop.

Department of Mathematics, Technion

The program at BIRS was definitely first rate. The organizers did a wonderful job and the list of speakers was truly impressive. The interaction between convex geometry and harmonic analysis was very interesting, but this brings me to a related point. While I enjoyed the program greatly, looking at the list of programs I was struck by the nearly complete absence of activity in classical harmonic analysis and related fields like additive combinatorics and geometric measure theory. With Izabella Laba, Akos Magyar and Malabika Pramanik at UBC, and Eric Sawyer in McMaster, among others, it should be possible to organize an excellent program in Banff with focus on modern trends in harmonic analysis. While the PDE end of harmonic analysis has been thoroughly represented at Banff, other areas of harmonic analysis have not been featured nearly to the same extent and I believe that it would be very time to do something about that.

The meeting in Banff was great : good organization, good staff, good mathematics, and certainly very useful, at least for me, and certainly also for most others.

The stay at BIRS was a perfect opportunity to keep the contact to the other experts in my research field. We started discussing a new research project which looks rather promising. The contact to some people from Case Western University helped me to find the appropriate place for my PhD student for a stay in the USA.

The participation in the workshop "Harmonic analysis in convex geometry" enabled the continuation of two research projects with Matthias Reitzner (Univ. Osnabrueck) and Paul Goodey (Univ. Oklahoma). We made substantiall progress towards completing at least one new paper during the time in Banff. Also two of my graduate students (Thomas Wannerer, Manuel Weberndorfer) had the opportunity to participate in the workshop which has lead to new collaborations with Wolfgang Weil (Karlruhe Institute of Technology) and Rolf Schneider (Univ. Freiburg). This will undoubtedly have a positive affect on their future job prospects after they finished their PhD.

Institute of Discrete Mathematics and Geometry, Vienna University of Technology

There were several directions of research which I was less familiar with and the workshop provided the means to understand the technicalities of these sub-areas. I also had the opportunity to start a new research project. Its basic idea originated prior to the workshop, but it took off the ground while I was in Banff. Obviously, the atmosphere was very stimulating and conducive to research and I'm very grateful to BIRS for providing it. I also made new contacts in my field and became aware of the work and interests of several young people who are just starting out in their career.

As always when I am at BIRS everything was perfect and the scientific program was excellent. Thanks to my stay there, I was able to continue discussions on a project I have with 2 other colleagues that were also attending the workshop and we made quite some progress during the stay. Also, I did tentatively start two new projects with 2 other colleagues. The talks during the workshop were very interesting and gave me a lot of new ideas to think about. Alex, Artem, Dima and Vlad did a great job and so did everybody at BIRS!

This workshop allows me to learn recent contributions in convex geometry and its connection with other fields, such as quantum information theory, random matrices, etc. I also have opportunities to present my recent work on quantum information theory where we used a lot of techniques from convex geometry. Besides, I also have wonderful discussions with some great mathematicians and have chance to know some new mathematicians. This workshop definitely benefits me in my future research of convex geometry and its applications. I really appreciate your excellent work for organizing and holding such a wonderful workshop.

School of Mathematics and Statistics, Carleton University

This workshop was one of the most inspiring ones that I ever attended. The seemingly diverse range of topics are indeed all tightly knitted together, and I think a beautiful big tapestry is being woven right at this moment. Listening to physicists Bouchard and Klemm, and number theorists Rodriguez-Villegas and Stienstra, and talking to Zagier, I found a hint that I have been searching some time. I need to sit down and think through it, but it looks very promising. I was also immensely impressed by the talks of Brown and Walcher. Bouchard and I will be organizing our own workshop later this fall in your institute. The topics we have chosen are getting a lot of attention and excitement now. The enthusiasm is increasing. I'm so glad to be able to attend the last week's workshop, where I received inspiration and excitement. Thank you for providing this great opportunities to the world!

Mathematics, University of California, Davis

This was a fantastic workshop, with some very good talks. I particularly enjoyed having Prof Zagier in the audience, who always asked pertinent questions and made the speakers explain their work better. I also had a number of very useful conversations with Prof Zagier which I think will move my research forward in interesting ways, in particular in the search for finding modular forms in the noncommutative DT series of the local projective plane. Discussions on this subject with Prof Rodriguez Villegas were also very useful. At the meeting, I also had very good discussions with Prof Doran about one of my PhD students' work, including discussing a job offer to this student from Prof Doran.

The workshop was a huge success. We indeed worked very hard with six lectures from 9:30am til 9:30pm, lectures were so interesting and nobody complained about the heavy schedule. We really felt that the barrier between mathematics and physics is coming down and both camps now find the common language. Modular forms occupy the central roles in mathematics, but they appear frequently in string theory landscape, and we would really like to understand conceptual reasons why modular (automorhic) forms play such important roles in physics. Many participants urged me to apply for the squeal to this workshop at BIRS in two years time. I plan to do so. This past workshop was partially dedicated to Don Zagier for his 60st birthday. Thank you very much.

It was a very stimulating workshop that you organized, in a fabulous location and with spectacular scenery, lots of snow on the mountains and yet mild sunshiny weather. Couldn't have been better! Yes, the time at BIRS was very stimulating and the interactions will lead to some new projects and hopefully to a resolution of the origin of the MJO. Thank you for making the excellent facilities of BIRS available and thank you to your staff for facilitating a very successful workshop.

Thank you for providing the resources for the workshop. They were exceptional. The workshop itself was very beneficial from a variety of perspectives. I'm an observationalist that will be involved in a large international field campaign to study the Madden-Julian Oscillation and I had many fruitful discussions with other scientists studying the problem from theoretical and modeling perspectives.

This workshop was one of the most valuable meetings that I have ever attended. Through feedback from other workshop participants, I sharpened the focus of my current research (some of which was inspired by the Banff workshop of two years ago). I also made new contacts and received suggestions/references for a future project. I learned a huge amount from the other workshop participants about observations, modeling and theory of tropical convection.

Mathematics, University of Wisconsin

This is my second time participating in a BIRS workshop. I enjoyed it even more than the first time. During the workshop, I had chances to clarify research issues that had been confusing, forge new collaborations, and reach a much clearer picture of where our field is and what the main challenges are than before the workshop.

MPO, U Miami

I also think the organisers did a first-rate job. The conference was of much interest to me. I was very much encouraged by the efforts of the younger researchers in the field. I have already started to follow up a couple of ideas that arose as a direct result of discussions at BIRS, I hope these lead to some fruitful outcome. I hope BIRS will continue to support Algebraic Graph Theory and more generally Discrete Mathematics in the future.

Coming to a BIRS conference is always stimulating, both due to the surrounding environment and the mathematical content. During the Algebraic Graph Theory conference the talks covered a wide range of topics that were insightful and have motivated me to pursue some new directions in my research (particularly the talks by Sebi Cioaba and Willem Haemers). Also during the conference I started a new collaboration with Alyssa Gottshall, Kara Greenfield and Michael Young on a problem about a game played on graphs and in the space of a few days we made tremendous product (what would normally have taken several weeks or even months outside of BIRS).

My participation in the BIRS workshop had a high impact on my current research. I had the opportunity to discuss my current research with other people working in the same area. From this discussions I had new interesting ideas regarding my research.

Since there were not too many colleagues working in numerics at this conference, the most important impact on my research was to see what the important problems in the field of Ricci flow and related topics were. We are working in numerical methods for Ricci flow (a PhD student and I) and I could collect a lot of problems which should be attacked numerically. Also the discussions concerning applied geometric evolution equations have been very helpful, specially the organizers Eric Woolgar and Gerhard Huisken pushed forward the connection between theoretical and applied studies.

Applied Mathematics, University of Freiburg

It's a wonderful experience for me to participate BIRS workshop on "Geometric flows in mathematics and physics", April 17-22. I attended all the talks, and engaged many fruitful discussions with other participants. The talks are of very high quality, topics touch the most recent development in the field. More importantly, what I like the most is the stimulation interactions with people there. I also worked out with my collaborator Lei Ni during the stay in BIRS. We made some good progress on the problem we have been working on for some time. In conclusion, it's a very successful workshop!

Heard some nice new ideas, and met some interesting people. Could present my own work in a talk. It was also nice to talk again to people I met before at other conferences.

I will remember the discussions at Banff, and some of the people I spoke to in person for the first time, for many years; they are having an important influence on the directions of my research.

Yes, this workshop did impact on my research, indeed. It was a great and discussion loving atmosphere with great colleagues. Most of them were known to me in one way or another. However, there were also a few new contacts that I could establish and from which both sides will benefit. I have rediscussed seemingly established knowledge and learned about other point of views. I cannot yet tell whether these discussions will on long term lead to new collaborations or additional papers. However, I also had the opportunity to let colleagues know about job opportunities in my lab. This workshop was excellent and outstanding, which is certainly not only due to the attending scientists but also to the nice atmosphere in BANFF and the excellent facilities.

I learnt a considerable amount about the current state of the art in techniques such as single particle tracking and two photon imaging. It was very useful also to be introduced to the main players in mathematical modeling in my field. These personal contacts will make it much easier to interact in future.

Pathology, Oxford University

I am very glad to have participated in the Workshop on Quantum Control, which gave me a rare opportunity to know the research achievements in interdisciplinary fields of quantum control. At the same time I also found that some problems existed and stimulated me to have new ideas about the study. I’ll be happy to take part in a similar workshop next time. In this workshop on Quantum Control (QC), I notice that there are 17 people who are mathematicians, which is half of the total number of participants. Indeed mathematics plays a very important rule in QC, I think, especially in controllability, observability, filter, estimation, identification, stability, convergence and new control method proposed, etc, all of which should combine the mathematics with the individual physical or chemical systems. I am impressed that only those people who are able to combine their own specialty with other specialties such as quantum physics or chemistry, can do well the QC. Owing to the interdisciplinary, QC concerns the physics, chemistry, mathematics, computer science, system control and engineering. The meaning of a terminology in one field could be understood as another meaning in other field. I find there exist some confusion or mix up in some terms. One example is “optimal control”. Optimal control is a terminology in system control field, which means a kind of special control theory or method called “optimal control (theory)”. One can say that all different kinds of control methods are not optimal except the optimal control (method). So people often want to optimize the parameters of other control methods or controller and do so indeed, which produces another terminology called “control optimization”. Another situation at present is one creates a new term, but the new term is in fact not new and it has the different meaning in one existed. These stimulate me to want to write a paper to describe and set forth the basic concepts, general configuration and various kinds of control methods in a quantum control system. I believe that quantum control belongs to the system control category or field, only the system is a microscopical one.

The workshop was phenomenal! In addition to continued I met several mathematicians/scientists whose work greatly coincides with my own, particularly Christiane Koch. Based on discussions with Robert Kosut during the workshop, we identified a promising new approach for robust control of uncertain quantum systems. Overall, the workshop was very motivating. It was quite refreshing to learn that mathematicians are also looking at quantum control protocols from a rigorous perspective.

Scalable & Secure Systems Research, Sandia National Laboratories

I have to be absent from the workshop due to lack of travel funds, but from the online discussion, I obtained helpful research insight and a possible collaboration on project or papers. I'm involved in the field of quantum control for many years, and I wish to have the opportunity to do research concerning this topic. Quantum control always stand in the front of other subjects, and it has a great impact on my applied mathematics major. Thanks again for the wonderful workshop at BIRS!

Mechanical and Automation Engineering, Chinese University of Hong Kong

BIRS significantly impacted my current research and career development. Several new and interesting insights were gained through meeting others in related scientific disciplines. Future directions for my research will be affected by the subjects discussed within the workshop. Connections exploring new research areas were helpful in directing future research for myself and the entire multiscale research community.

It was a very very exciting experience. I would certainly look forward to another "follow-up" workshop possibly in a year. For me, it has opened up the "possibility" of new collaborations and rejuvenated the process of resuming some not-so-old collaborations.

The recent workshop at BIRS impacted my current research in several ways. (1) I was able to interact and network with leaders in my field to understand commonalities in my research and potential for collaboration. I also was able to ask clarifying questions about other researchers' work. (2) I was able to discern with more clarity the outstanding research questions in my area. (3) I was able to see and begin to address the difficulties in connecting two sometimes disparate fields: engineering and mathematics, as both communities have different needs, interests, and language. Also, the workshop most likely helped my job prospects as I will eventually pursue a faculty position. Being able to network with the participants will help me have a better name when I go through the interview process.

As a 4th-year graduate student, I attended this workshop for educational purposes, although the topic was not completely directly related to my current research. In that respect, I did not have the necessary hindsight/knowledge to contribute to the discussions or engage in future work for now. However, the workshop was very fruitful, in that it successfully opened a constructive dialogue between engineers and academics, through the presentations and the evening discussions. In addition, I certainly made new contacts that I wouldn't have had otherwise.

Applied Physics and Applied Mathematics, Columbia University

I had a great time at BIRS! I came away with at least one new paper with V. Vertesi and D.S. Vela-Vick, in which we prove that the Legendrian invariant defined using grid diagrams agrees with that defined using open books. I started a new project with C. Manolescu, in which we identify the contact invariant of a contact surgery in his combinatorial formulation of HF+. I also began a project with L. Watson which could lead to an understanding of Szabo's spectral sequence in terms of holomorphic polygon counts.

Thank you for your kind e-mail which perfectly illustrates why BIRS works so well : attention to detail, great organization and a genuine care for the work done by mathematicians during their stay. Last week's meeting was really excellent from so many perspectives. Some amazing talks with deep results, a few excellent talks by more junior mathematicians, a great variety of areas represented allowing (formally and informally) to have an overall vision of what is in fastest expansion, and many small groups working on projects until late at night. Every time we organize one of these, we are amazed at how well this works. With my co-organizers we will write to participants to know what results came out of last week and it will be a pleasure to write up our report during the summer. We are really grateful to BIRS as this was the 3rd edition of this conference around interactions between contact/symplectic/geometric topology.

The workshop was very helpful for me since it allowed me to get up to date with the latest developments in my field, even with the internet it is still very helpful to hear experts talk about their latest research. I also used my time at BIRS to finish a paper with Stefano Vidussi. I am very grateful for the time at BIRS.

As always, my time at BIRS was amazing. The talks were excellent, the participants engaged, and the organization impeccable. Almost without fail, a BIRS conference leads me to new avenues of research. This past week was no exception, as a chance breakfast conversation led to a new result and has opened up an exciting direction in my research and a new collaboration. In fact, the talk I gave last week was based on a theorem that was dreamed up at the conference 2 years ago. In addition to the theorem, that conference also led to a fruitful ongoing collaboration. The posters sprinkled around the Banff center aren't just propaganda - it truly is an inspiring place. I also wanted to thank you for accommodating my early arrival. This allowed me and a collaborator - Olga Plamenevskaya - to make serious progress on a project which, thanks to the support of BIRS, is nearly complete. I am extremely grateful to have access to such a special place.

This conference was a great opportunity. As a graduate student, it is important to be exposed to the most current topics in research, especially what is not published. It was very helpful to hear about what people have been working on, both through lectures and speaking with people. This process introduced me to many new people and gave me perspective on how people are thinking about the field and its current state. I am hoping that this will help improve my job prospects when I apply for postdoctoral positions next year, as I was given an opportunity to give a talk, which exposed me to people who had either not interacted mathematically with me before or seen me give a talk. One of the most valuable aspects of this conference was that it got me inspired to work more on my research. In fact, a colleague that I was already collaborating with mentioned something to me at the conference and I was able to come up with some results on the plane ride home.

My participation did impact my current research. I had clarifying exchanges with colleagues regarding my work in progress and learnt about very interesting work in progress of other researchers, which stimulated my own research. Last but not least, I started a new collaboration during the workshop.

Dipartimento di Matematica , University of Pisa

During the BIRS workshop I started new research projects. I was able to talked to two experts on other related areas of research, which was quite useful, e-mail communication can only take you so far. Moreover, to know what other experts were working on was very informative and it put things into perspective. BIRS is an amazing place to do math. Thanks to all the staff.

Mathematical Institute, Oxford University

I had a great time at BIRS, most of the talks were quite closely related to my research area, and I benefited a lot from them. Apart from the talks, I managed to collaborate with two of the participants; David Shea Vela-Vick and John Baldwin, and proved a new Theroem that finishes a long-standaing project of mine about Legendrian invariants in Heegaard Floer homology. In different settings there were three invariants defined for Legendrian knots in Heegaard Floer homology. One is defined by Ozsvath, Szabo and Thurston for Legendrian knots in the standard contact structure in SÂ³. The other is defined by Lisca-Ozsvath-Stipsicz and Szabo for arbitrary Legendrian knots in an arbitrary contact structure. Both of the above invariants are in knot Floer homology. The third one is the contact element in the sutured Floer homology for the complement of the Legendrian knot defined by Honda, Kazez and Matic. In my thesis I understood the connection between the two later ones. In BIRS we managed to prove that the first and the second are the same in the standard contact structure in SÂ³. Thanks a lot for the inviting me to this wonderful event, I hope to be able to go there more.

I finally understood what all the talks on naturality in Heegard Floer homology were about - BIRS seems to stimulate more open, honest admission of gaps and mistakes in math. I did some crucial work with a collaborator on a joint paper - possible only because we were looking at the same piece of paper in the same room. I had fruitful discussions over lunch, dinner, and beers, with many potential collaborators - clarifying who had already done what work, and what would be potential projects.

I had a fantastically stimulating and enjoyable week. I had an opportunity to meet with nearly all people in the world who are thinking about the same problems as I. I enjoyed listening to all the talks and I enjoyed giving my own talk to such a receptive audience. It certainly gave a boost to some of the collaborative projects that I am involved in. Whether new project originated exactly during this week is a little too early to tell. Possibly. Certainly the workshop acted as a catalyzer for my favorite scientific discipline. My former student gave a presentation and it was well received. Whether it will have a specific impact on his job prospects is, again, a little difficult to tell. It certainly was a very useful experience for him. Thank you for the opportunity to spend a week doing my favorite work in such a relaxing and stimulating environment!

The intimate setting of BIRS created an atmosphere of mathematical discourse between myself and colleagues that was virtually unmatched by other workshops I have attended. I came to the workshop with some vague ideas about a certain calculation I was working on - the intense discussions that followed now provide me with a blueprint to work from!

Mathematics, Massachusetts Institute of Technology

I used the workshop to present work by my PhD student Pornrat Ruengrot. The work is of a speculative nature, and the BIRS workshop was an ideal opportunity to seek ideas from an audience highly specialized in this area as well as to seek reassurance that we are on the right track. As a result I was told about two pieces of work, one unpublished, which are very relevant to his research and resolve one problem that we had been working on. The workshop also allowed me time to talk in depth with some experts on the representation theory of finite groups of Lie type, which has been very valuable in an ongoing research problem on blocks with elementary abelian defect groups of order nine. It also allowed me time to work with a Japanese collaborator in the same research. Overall, the workshop brought me into contact with many of the key players in my field of research, all concentrating on a specific set of problems. I feel that I am fully caught up now with current developments and have a clear idea of what people are working on right now.

The conference gave me the opportunity to have two short, good discussions: one with Michel Broue about the ongoing project by him, Bhama Srinivasan, and myself; the other with Britta Spaeth about the current state of a question on Harish-Chandra induction and Galois actions which she and I considered two years ago. The intimate, relaxed setting of Banff gave a directness and immediacy to mathematical discussions. The range of talks was excellent, going from the intricate, difficult nailing-down of individual cases needed for current inductive proofs to bold, engaging, new examinations of basic questions. We all went home with much to think about.

This was a wonderful and highly productive workshop, which provided me with considerable new insight into relations between my own research and that of the other participants. As an immediate result of my participation in this workshop, John Harper (another workshop participant) and I will certainly publish a new article containing a lovely little theorem, which the other workshop participants helped us to realized that we had almost finished proving.

Mathematics , École Polytechnique Fédérale de Lausanne

The workshop was extremely informative and inspiring. In particular I had the chance to talk to two of my colleagues about a joint research project. Such a workshop is a perfect opportunity to advance pending projects. Meeting your collaborators at an inspiring place and having enough time for discussions is extremely helpful.

Last week I stayed a week in Banff BIRS to attend Global/local conjectures in representation theory of finite groups. First of all I really thank the BIRS for such a wonderful hospitality, and also for such a nice opportunity to do wonderful mathematics. More precisely, I experienced the following: (1) I could communicate a lot with Charles Eaton (Manchester, UK), with whom I talked about one of the most important and interesting conjectures/problems in representation theory of finite groups. It was on Alperin's weight conjecture and also Broue's abelian defect group conjecture for a particular blocks with elementary abelian of order p squared. By the way, Broue attened this meeting in BIRS, and Alperin did not but his name was on the list at the beginning. Actually, because of this meeting in BIRS, Eaton and me have started our collaboration on the subject. (2) I could talk a lot with Britta Spaeth (Aachen, Germany) on our mathematics. Especially she and me discussed much (so-called) Dade-Glauberman-Nagao correspondence, which is also one of the most important problems in representation theory of finite groups. Dade was by the way one of the participants in this meeting in BIRS. The discussion with her was so efficient and useful for my research. (3) I spoke with Gerhard Hiss (Aachen, Germany) a lot. We talked on Donovan's conjecture for a particular p-group say elementary abelian of order p squared. We talked also on the classification problem of blocks of finite groups up to Morita equivalence under a mild hypothesis. (4) I discussed block structure of finite groups of Lie type, with Michel Broue, Paul Fong and Bhama Srinivasan. It was also quite important and useful for my research. Finally, I really would like to thank the BIRS for the meeting. For me it was the second time to be there (the first time was in October 2003, when Alperin, Broue, and Cliff organized a meeting in BIRS). I really appreciate it. I wish this kind of program would keep on going, and hopefully I would like to attend it again in BIRS. Thanks a lot again.

Yes, I have learned about the "basic set" conjecture directly from the people involved in that, and I am already thinking on a way to reduce it to simple groups. If I succeed, this of course will be a collaboration with several of the simple group people that attended the conference. I helped Britta Spath to find a missing piece that she had in a key paper that she is writing now (and on which she spoke in Banff). I met Evseev and was able to think about his conjecture more properly. One of the most important things at the workshop was an informal meeting that several had, in which the map of the road to finish some of the conjectures was drawn.

This was a remarkable workshop in the placement of the topics, in particular of the well-prepared two-hour series, which were distinct but had interesting overlap. This was the best "snapshots of a field" that one could imagine. I wish the talks were all taped so that they could be a resource for graduate students. I look forward to building on the recent breakthroughs of Arone-Ching and Behrens. I will take the clear picture gained from these lectures back to my home institution, where it is likely that my colleagues and I will build on this insight in our own projects.

Mathematics, University of Oregon

The impact on my research is quite large. I learned from Shigeo about a recent preprint "about a minimal counterexample for the Alperin-McKay conjecture" from Masafumi Murai (related to my own project, some of my minor results are also proven there, but with completely different very inspiring methods.) Gabriel Navarro proved for me a congruence, by which I can adapt the reduction theorem for the Alperin-McKay conjecture to the Isaacs-Navarro refinement. It enables me to strengthen my results. I discussed some stuff with my former colleague for our ongoing project, where we want to prove that PSL_n(q) satisfies the inductive McKay condition, and about possibilities to generalize elder results towards the inductive Alperin-McKay conjecture. Also with some other participants I had some nice interesting conversations, which were very inspiring and will be helpful for my further research.

In my view this was a very successful workshop. The participants were a judicious mix of senior, mid-level and junior researchers. It was also focused on a topic familiar to all the participants. As a result I was able to learn from every lecture and have discussions with most of the participants. My current research, which I presented at the workshop, is connected with the work of three of the participants. Thus discussions with these participants led to new insights and ideas for my continuing research. It was also interesting to meet some of the junior participants for the first time and to learn what they are working on. In turn some of them asked for information regarding my talk, such as copies of my slides.

The workshop's scientific program was focused and well-organized. All the talks were interesting (in fact it was the opinion of several participants including non-speakers that I talked to that all the talks at the workshop were uniformly of high quality!) Several important results were announced during the workshop (my co-organizers and I will write about them in details in the report), some by young participants. Following these new developments, we had informal discussions to coordinate the efforts of researchers from several countries to work on a set of fundamental conjectures in the field. I also had fruitful discussions with my collaborators (including Gabriel Navarro and Gunter Malle) on ongoing joint research projects.

The workshop was useful to learn about how mathematicians can play a role in helping to improve RT. I was reassured that there is a great opportunity to collaborate to find a cure to cancer using RT.

The workshop was very beneficial to me as it provided me with the chance of meeting influential people in my field and hearing their different point of views. As a student, it gave all new insight into the field and how it is going to grow in the coming years.

It was a great workshop! I learned a lot from other attendees. Most importantly, I established a couple of potential collaborations with our OR colleagues.

Department of Radiation Oncology, University of California, San Diego

Computer Science Department, University of British Columbia Okanagan

The workshop helped me engage with researchers in the field and get new contacts. It also helped me get feedback about some of the research work I had been doing. It was definitely worth it!

I always enjoy BIRS workshops. The environment is great for collaborations and the invitees are always a select group. The talks and the discussions are high quality and stimulating. I always leave here feeling I learned something new and I get energized to do further research. This particular workshop gave me significant feedback on my research directions and resulted to nice connections being made between my work and research in related fields. It exposed me to interesting new problems in my field and directions that are very interesting and relevant to my work.

The workshop was certainly successful in the sense that it gave me new ideas and allowed me to meet new people in the field. Having said that I think there is room for improvement regarding - discussions, I know this is up to the organizers but perhaps there is something BIRS can do to "force" more discussions so the meeting does not run the risk of becoming "yet another fully packed conference where people are preaching to the converted". Please do get me wrong the quality of the speakers was outstanding but it would have been nice to have a format that allowed for more informal discussion aside from the quality time over diner and in the lounge in the evenings. - involvement of graduate students and PDFs. I think this meeting could have done better in having more graduate students participate. The main organizer brought some students but that was about it. I think this is a missed opportunity and perhaps it would be good that BIRS is more proactive in that regard.

I would like to thank you for giving us the opportunity to hold our workshop at BIRS. To our mind, it was a great success as also all participants confirmed to us. Most of the leading researchers in the field were present and the talks were all of very high quality. Numerous very fruitful discussions took place, and I know of many new collaborations which were started during the workshop. Let me also add that to me personally, BIRS has a special atmosphere, which I find extremely inspiring. I think - besides the high quality of the workshops - it is the unique combination of excellent organization, very friendly and helpful staff, comfortable rooms and lounge, and quiet and beautiful surroundings.

The workshop was fantastic and I really appreciated the opportunity to attend. The setup of BIRS was perfect for stimulating conversation in a fun, friendly environment. The workshop itself gave me an expanded appreciated of the field, but interestingly the most productive portion occurred during the two extra days (Fri/Sat night) that I was able to spend at BIRS. During that time, Sebastian Funk and I were able to make real progress on a collaborative project for reconciling differing results from branching process and network theory. Thanks for making BIRS the place it is.

What a wonderful week! We learned a lot, made great connections, and had a wonderful time. Thank you, thank you, thank you!!!!!

What a wonderfully organized meeting at BIRS! I made many new contacts and spent a great deal of time discussing both new and ongoing projects with individuals at the meeting in formal and informal sessions (including over our on-site meals). It was a bit like going to summer camp with all of my nerdiest friends and it was fabulous! Lots of fresh insight was gained. In fact, some colleagues and I sketched out a plan for a future research proposal on syphilis in the lounge one evening after the sessions had ended. One of my graduate students also attended the meeting and I feel that it was an invaluable experience for her. It was really exciting to see her become involved in active discussion and debate during the group sessions. The small meeting size really made it possible for graduate students to actively participate and engage with faculty and scientists attending the meeting.

I would say my attendance had an effect on the way I have been thinking about my own work. I am a novice in infectious disease modelling so it was very beneficial to see established and rising experts in the field impart some of their own views on modelling. Many of the formal presentations made me think more about and afforded me a better understanding of the connection between my own work and recommendations for and implementation of public health policy. I enjoyed meeting many people I would not get normally get the opportunity to and I also benefited greatly from several individual conversations, from which I derived new insights and also an awareness of some of the existing modelling literature that I previously knew nothing about. One particular conversation has given me a different perspective on the treatment rates in my own model and their epidemiological relevance. I particularly appreciated the theme of the workshop --- control of persistent infectious diseases is something that often gets overshadowed by epidemic outbreaks and so it goes too with modelling. Mathematical issues differ as well between these two situations and, as a relative newcomer to the field, it was useful to see models not devoted to epidemic outbreaks. I did not forge any new collaborations but I was able to get some solid work done on a paper I was already collaborating on with colleagues who also attended the workshop. Perhaps what I found most beneficial and encouraging was the fact that several of the models presented adhered to important epidemiologic principles without becoming unduly complicated mathematically. I come from a fairly strong math background but am still learning how to apply that in an epidemiologically meaningful way. It was therefore a refreshing reminder that fancy math needn't always provide the optimal answer! Finally, I would like to express my gratitude to BIRS and the workshop organizers for the opportunity to attend this workshop. I enjoyed it immensely and found it very rewarding.

It was extremely useful for our current research. The meeting was a great forum to see what the community is actively working on, and importantly, to identify new questions and applications that require study - many of which we can tackle through collaborations made at this workshop. The best discussions surrounded issues raised by researchers from different fields. The discussions shared in this meeting generated interesting ideas for our group, many of which I think will develop into fruitful collaborations.

The quality of the workshop is exceptionally high. It will surely bring an important impact on my current research. Through the talks, the informal discussions greatly facilitated by the organization, such as the dining room, lounges, the bar, the party and walks and sightseeing. I came back with at least two new research projects, including one with a new collaborator. During the conference I have also contacted a few people to seek possibilities of hiring my students as future postdocs. This may well end up a solid offer. The impact of such a workshop can't be under-estimated. I can safely say so from many of my professional experiences over many years. Thanks a lot for accepting to hold the workshop at your remarkable center.

Mathematics, Universite d'Angers

My participation in the BIRS workshop impact my research since I could hear new results. I could also get a fresh insight and meet people I wouldn't have had otherwise.

As an Engineer working in control applications, my main interests were numerical methods for the HJB(I) equations. This workshop has given me the opportunity to meet some of the major contributors to this field. Besides the comprehensive talks, the informal discussions provided me important insights on some subjects and some problems to pursue. These informal discussions would be harder to achieve by electronic contacts or in larger meetings. This meeting was also useful to establish preliminary contacts for future collaboration, with new meetings already scheduled for the short-term.

I had a very productive time - Diogo Gomes and I started and made substantial progress on a paper about numerical methods for mean field games.

My participation in the BIRS workshop has exceeded my expectations. I have found the whole content very useful and in particular the Tutorials offered by four of the participants. I was familiar with one of the themes treated in the tutorials but not that much with the other three. I have learned a lot from them and from the discussions that came out during these tutorials. I think this was a very good start for a workshop where different approaches on the numerical treatment and algorithm design for the approximation of the solution of Hamilton-Jacobi equations are studied. On the other hand the wide variety of the applications and results presented during the rest of the participative talks has given me an insight into some problems I was not familiar. From my experience, it has been the kind of research meeting that you start with some ideas on your mind and leave with some of them solved and many other new ones in project. I left BIRS with much more enthusiasm to continue working on this field. I have met new colleagues that I can understand in a similar "mathematical-numerical language" with common interests in specific applications. We will hopefully start new collaborations in common projects in the future. This workshop has definitely had and positive impact in my research interest. Thank you very much for the opportunity of having this great experience.

This was an outstanding workshop with a large fraction of the leading researchers in the field. It was well-organized in every regard and the BIRS facilities were ideally suited to its size and scope.

Department of Physics, University of Texas Austin

The workshop was restricted to a small (20) group of leading experts in this nascent field. This was great. It allowed ample opportunities for long, detailed one-on-one discussions between knowledgeable experts. I learned of many important advances achieved in rival labs., and picked up many valuable ideas for new research directions. I am happy I decided to attend. Banff is highly unusual in providing nearly ideal conditions for such well-targeted workshops in rapidly developing research areas. In the North American continent, its only rival is Aspen.

Physics, Princeton University

The area of ergodic optimization was peripheral to my research. This well-run, intensive event has considerably increased my interest in this subject. I now view some aspects of my research from a different perspective, and I have established contacts with key people. This second visit to BIRS has confirmed to me that this is one of the very best institutions in which to carry out programmes of this kind.

School of Mathematical Sciences, Queen Mary University of London

The workshop covered some of the very new research areas in linear algebra, graph theory and combinatorics. I learned some of the new research topics on eigenvalues of laplacian and signless laplacian matrix. I had some very interesting research talk with some of the attendees. It provides me some new ideas about the second the largest eigenvalues of some special matrices.

The workshop was a fantastic opportunity to network with other people in my field, and particularly to put names and faces together. During the workshop I was able to focus and found a new extension for research that I had been working on and was able to share that with another participant at the workshop.

It was a rare moment in my academic life, meeting some of the leading and influential researchers in my area of interest. The lectures were exciting. BIRS facilities are simply excellent! The organization was superb. Special thanks to Hadi Kharaghani and Richard Brualdi.

This was a great workshop with many interesting and well presented talks. There were participants from four continents and more than ten countries and we were blessed with having Richard Brualdi as an organizer. Thank you very much for making such a great facility available to mathematicians.

Math and Computer Science, University of Lethbridge

It is early to say, but I learned a lot of new material. I had discussions with many colleagues and this will certainly affect my current research.

The DFT workshop was a great experience for me. It's a new field I'm trying to learn, and the workshop was a perfect opportunity to hear a variety of talks and meet experts in the area. During the talks I downloaded about 2 dozen articles must-read articles! I appreciated both the tutorial talks as well as the ones on current research - that is a good combination. Also, the informal discussions in the lounge and at meals were very valuable.' Logistics and hospitality were tremendous. In spare time I went swimming and attended the mid-week classical concert - a real treat.

I enjoyed very much to follow the workshop. I had the chance to discuss and exchange ideas with experts in my field, but also to follow and have an overview of the research and the aims of other scientists working in the same field (density functional theory) but from another prospective. I came back home full of ideas and with a strong motivation to continue my research.

This is a wonderful workshop. During the workshop I talked and discussed with several participants who have some intention to collaboration on our common interest. I am sure that my participation will impact my research and affect my supervision to my students directly or indirectly.

Institute of Computational Mathematics ans scientific/Engineering Computing, Chinese Academy of Sciences

This is a great workshop. It is on a topic I am familiar with, but I learned new ideas from it. And hopefully some new projects based on the workshop.

I visited the Games of No Chance workshop in January 2011 and had a wonderful time. I was able to present the work I am in the middle of for the perfect audience. Some of the main researchers in the field showed great interest in my work. In fact, I was told that it had opened up a whole new territory of combinatorial games. If I would not have come to BIRS, I would not have had this great feedback. Also, as a consequence of this workshop I am currently working on two joint papers that would not have come about otherwise. Thank you so much for your wonderful work. I am most grateful! I presented two papers at the conference. One is submitted to TCS in May, the other I plan to submit to the GONC proceedings in August (this is a joint work with Johan Wästlund). The conference has also resulted in two ongoing projects with participants at the workshop, one with Michael Weimerskirch and the other with Aviezri S. Fraenkel. Both these projects are intended for the GONC proceedings. Both these projects resolve a question which was posed at the conference.

...Thank you very much to the organizers for this opportunity to come to this BIRS event, which was just great for me: - for opportunities of meeting people from combinatorial game theory (for which I am an extreme beginner...), - for opportunities of discussions with people with solid background around undecidability in partially observable games, - for opportunities of meeting once more my friends of Monte-Carlo methods; - for the opportunity of playing games against a pro human player (including a won game as black against a 9P player, thank you so much Martin for this opportunity! there are still not so many wins against pros as black and this is a great new result due to this BIRS event) - for the beautiful environment in Banff and the scientific paradise at BIRS. This was my first time at BIRS and it's as good as Dagstuhl - two great places for learning and doing research. I'll remember to acknowledge BIRS in my next publications.

It's too early to say for sure - several new projects have begun at BIRS, and I hope that of those, at least a couple will continue strong...

SheepDogInc.ca

The workshop will have an impact on my research in the field of math teacher education and my work with teachers. The discussions inspired my thinking in terms of how I can expand the work I do. It was a very productive workshop.

...Indeed: I greatly profited from the workshop. Thanks very much to the staff at BIRS for its great job.

Mathematics, HU Berlin

This was one of the most productive meetings I have attended. The setting was inspiring.

I think the workshop was very useful for (a) getting a sense of the "lay of the land" with regard to international efforts at professional development, and (b) thinking about ways to develop the theoretical underpinnings for such work. I will be thinking more sharply about the second issue, and writing about it.

Education, EMST, University of California, Berkeley

This is a memorable experience in a very well organized and beautiful surrounding. In fact, I have enjoyed the experience so much that I plan to submit a proposal as well. The scientific program was high quality, and BIRS an excellent avenue for workshops and meetings. Except for the little cold, it is perfect.

Superb conference, outstanding speakers, and very timely scientific content. It's early to say if collaborations will emerge, but they probably will. The conference strengthened contacts with a few people, and this will encourage further discussions. It was good to hear about the latest results. After my presentation, one participant suggested a stronger version of a probability lemma that we use in one of our papers. This opened up a new theoretical direction for me and my graduate student. We now have a more complete view of the existing results in that field (probability in Banach spaces and Rademacher chaos). We will know how to continue looking for those results, and participate in this sub-field ourselves. I also met many important people whom I would otherwise not have met. I advertised for an open postdoc position, and some participants suggested candidates for the job ...

Mathematics, MIT

... my stay at BIRS was simply wonderful. The concept of BIRS is ingenious; at conferences people disperse at the evenings and get to interact much less than at BIRS, where they share the meals and the living room with the wonderful beer selection. Interaction between the participants is much more intense, once they are "confined" to smaller premises. Also, doing science "on demand" simply does not work. The best way to go is the BIRS way: you just make the environment conducive and things then happen spontaneously. I wish we had such a facility in Australia, where, I feel, the money is spent in a much more luxurious but far less efficient way. No wonder Canada is so much ahead of us in science and technology. I was also impressed that the premises are low key (shared bathrooms work as good and save money!) but extremely comfortable with exactly what people need. The food was lavish, and my "only complaint" - actually my wife's complaint - is that I gained 3 kg, everything was so tasty! The staff were extremely friendly and helpful, especially the lady who took care of us and whose name escapes me at the moment. Also, the number of the participants is just right - large enough to meet many colleagues and small enough to be intimate and coherent. So no ideas how to improve anything - you guys are just doing everything in the best possible way. I hope there is no cost cutting madness in Canada - it would be a tragedy to ruin such a wonderful center by saving a few thousands, please resist politician's pressure to save money, scientists need BIRS!!!

The primary impact on my research at this point, just a week after the workshop, is a better appreciation of the work being done in areas closely related to mine. It will take 1/2 year to see whether the ideas and problems collected during the workshop will result in concrete collaborations and publications, but the workshop certainly brought up a number of interesting directions and potential collaborations.

Everything was very good, the facilities, location, workshop, staff. First class.

Thank you very much for the hospitality of BIRS towards the Math Kangaroo team. The food and the accommodations were excellent. The workshop has helped the team to reorganize in order to be able to help more students from grades 3 to 12 to be more involved in mathematics. It also had opened prospects of research on how students progress through the years in mathematics.

The workshop helped me to meet my colleagues and discuss the ways to work with talented or mathematically inclined students and promote mathematical outreach activities among them. This collaboration inspired new ideas about my research in mathematics education on mathematical problem solving strategies and problem composition approaches.

Education/Math and Stats, Memorial University of Newfoundland

My participation in the workshop impacted the area of my work in mathematics outreach significantly. I learned a lot about what other participants do. I met people and could have discussions on topics of common interest during the two days of the workshop. Yes, I established new collaborations with other mathematicians. We are working on papers and had some discussions on what exactly to include. Two of my students from Concordia University College of Alberta attended the workshop as well as gave presentations. This certainly will affect their job prospects since they gained experience in giving presentations and met other faculty members and researchers. The workshop may influence some hiring decisions I need to make in nearest future - at the beginning of 2011. Hospitality at BIRS is great. I can only say good things for the staff ... So much was done by BIRS - it made my work as an organizer and a participant so easy.

Thank you for the hospitality and for the facilities made available. Our organisation had a very successful conference on outreach of mathematical knowledge and instruction.

During the workshop I had the opportunity to meet people sharing similar interests and I got to know about the projects they are involved in. In the same time, I found out about initiatives they made in their regions which I will try to promote, in the future, in mine, too. For me personally, the workshop was very fruitful: I made new contacts, talked about further collaboration and gave me ideas about how to improve the things we do at regional level.

MATI, Ecole Polytechnique Montreal

The workshop was an unique opportunity for me to meet the people involved in the Kangaroo project. From this point of view, the input I received from them was extremely useful, the experience they shared gave an insight on how other centers manages to handle the growing administrative issues and the brain-storming brought forward interesting ideas. Overall, was an excellent occasion to share and build together. It definitively brought into my attention possible venues to extend the Kangaroo in our region.

New contacts, affects my students and the development of my professional interests.

The workshop had a definitive influence on my current research. New papers might originate from the workshop, as well as new collaborations,and reinforced links with previous acquaintances.

Laboratoire d'hydraulique Saint-Venant, Universite Paris Est (Ecole des Ponts ParisTech)

The last week in Banff was extremely fruitful, thanks to outstanding material accommodations and an excellent scientific program of talks. I met for the first time many colleagues, including french colleagues, I never met before. I work on high order numerical schemes, in particular finite-difference schemes. The applications are not only fluid dynamics (which was the subject of the meeting) but also many other fields: electromagnetism, imaging, etc. The Banff Center is really well designed both from the architectural and functional point of view. Running BIRS in that place is a great achievement for mathematics.

...I quite enjoyed my stay at BIRS. I found everything very well organized and was impressed by the quality of the facility you offer.

The BIRS workshop was wonderful. The site is magnificent, the lodgings are great. The scientific meeting was interesting, and thanks to the availability of the room downstairs, we were able to work very efficiently during the night with my colleague Robert Eymard and get some new results. Altogether it was a great experience.

Laboratoire d''Analyse Topologie et Probabilites, Universite d'AIx Marseille 1

I got in contact to people working in my area of research. Some participants could help with more information and some references to learn more about my topic.

This was truly one of the best meetings that I attended in my career. I was also one of the co-organizers and I must say that the organization in this case was extremely easy. The BIRS staff was very professional and we, the organizers had almost nothing left to do. I must say that BIRS is better (and I heard that opinion from other participants) than Luminy (France) or Oberwolfach (Germany). The workshop affected my research in two ways. First, I started discussions which will yield new collaboration with possibly two researchers. Second, my student J. Keating was able to attend and he probably learned more than what several courses could provide for him.

The workshop has been a fruitful experience in all respects (meeting new people, knowing knew results, possibly starting new collaborations)

The BIRS workshop on Nonstandard Discretizations for Fluid Flows has a great impact on my own research. Experts on this alive scientific field gave state of the art talks and allowed to get fresh insights in theory and applications. New contacts allowed me to start new and fruitful cooperations.

Mathematics, University of Magdeburg

After my talk, I spoke with two colleagues about an old problem where my methods may be applicable. During the conversation, we discovered that not only were they applicable, but given the work the two had already done on the problem, my machinery was the last step they needed to solve the problem. We are currently writing a joint paper on this. This represents a wonderful new application of my machinery, a fantastic result in Schubert calculus, and a new collaboration for the three of us. This alone would have made the conference worthwhile, and it was only a smart part of it.

... There was so much research going on between talks and in the evening that I would not be surprised if 10 papers come out in the next year from these collaborations. The common room was hopping each evening ... Thank you for the opportunity to come to BIRS.

This was my first trip to BIRS, and I had a wonderful time. I am not an expert on quasisymmetric functions, but having the opportunity to talk with the experts in the field, I have a better idea of where they fit in with the rest of my research. I was able to ask lots of questions and left BIRS with a healthy list of problems to direct my future research. I also owe a big thanks to Brenda for helping everything run smoothly.

Great meeting! Very helpful in many ways!

It has been a honour and a pleasure to be invited to the workshop on quasi-symmetric functions! I came from rather far (Italy), I have a special connection with Canada, since I got my Ph.D. in Montreal ... It has been a wonderful conference, in a perfect and beautiful environment: for me it is unusual to have so many people from the same area, it was really fantastic. And the organizers did a great job!

The setup at BIRS is really fabulous. At a typical conference, lots of time is spent looking for somewhere good to eat, and if you're not ready to leave for a meal after the last talk, you can miss out on having good company. Not only was the food at Vistas good, but even if you had something else to take care of at the start of meal time, there were always people still around to talk to, or others similarly arriving at their convenience. I also appreciated the efficiency of the buffet style service, which freed up time to be spent on research. Mathematically, the main outcome for me was that a collaborator and I were able to spend intensive time finally pinning down a proof that was causing us difficulty when we worked on it long distance.

Department of Mathematics, Bucknell University

Everything was excellent and every time I have been to Banff, I have been impressed by how conducive to collaboration the facility is. At this particular workshop, I learned about an area peripheral to mine and am not very enthusiastic about working in this field. I'm sure I will work with the participants in the future.

...The talks were all very high quality, bringing me up to date with the state of the art. In such a blossoming subject it is difficult to keep up with the rapid emergence of new results, so the talks, grouped together by themes were ideal to pick up the finer details, as well as to appreciate the bigger picture. This simply isn't possible in bigger meetings where the research focus of talks and attendees is wider. In addition, without the distraction of having to find a restaurant as would be at a usual conference, the lunch breaks and evenings were perfect for seizing mathematical opportunities that had arisen earlier, or to help to wrap up research projects with coauthors from abroad. Often both,in the lounge that was always busy with participants and their conversations, which sometimes went into the night. Of the 4 excellent BIRS meetings I have had the honour of being invited to so far, this meeting ranks number 1. In addition to learning about the state of the art and sharing my latest research, I also came much closer to finishing one project, and hope to have started at least one new one, with a variety of collaborators brought together by BIRS. I am in no doubt that this meeting has accelerated my research program by many months. Thank you for inviting me to be part of this fantastic meeting!

This was an incredibly useful conference. Several new projects have come from my interactions at BIRS. This was my first time visiting and I thought the facilities and organization were excellent. I especially appreciated the fact that we ate all our meals in the same dining room. This led to interactions with most of the attendees rather than just the ones I already knew.

Dept. of Math and Statistics, University of Vermont

The meeting did achieve its primary goal to foster interaction among topologists, geometers and combinatorialists all working in the area toric topology and geometry. I think it's fair to say that the meeting represented a significant turning point in overcoming language barriers among the three disciplines. Our report will reflect the fact that speakers all made a determined effort to be understood across the cultural divide. Indeed, it was a common sight to see mathematicians in related but different fields engaged in spirited conversations. For me personally, the meeting provided an extended opportunity to meet with my collaborators, Nigel Ray, Dietrich Notbohm and Matthias Franz. We spent two long evenings in the seminar rooms working on our project classifying weighted projective spaces. The workshop made it possible for the four of us to meet together for the first time since the project started. I managed also to have useful discussions with various participants about a paper Fred, Sam, Martin Bendersky and I completed just before the meeting on the topic of fan reduction for toric varieties. Various new questions about a construction used in that work arose and were resolved at the meeting. Our new project concerning the identification of certain moment-angle complexes as wedges of spheres, rationally, benefited from conversations we had at the meeting. Another construction on simplicial complexes, which allows the iteration of moment-angle complexes and polyhedral products, had its genesis at the workshop. The construction warrants further investigation and I have written already to fellow participant Carl Lee about the combinatorial aspects of the construction. We have received many enthusiastic and favourable comments from participants. Critical to the smooth running of the workshop was the extremely competent support we received from your excellent staff including Wynne, Brenda and Brent.

I found the conference to be mathematically compelling, and stimulating for the following reasons. (1) Generally, speakers in different areas made solid efforts to communicate how their topics informed on the main areas of the conference. I will take the liberty of pointing out several new structures which I learned about at this conference. (2) S. Lopez de Medrano and A. Verjovsky explained privately how spaces which we now call generalized moment-angle complexes (macs) give equivalence classes of natural dynamical sysems for which a theorem of Camacho, Kuiper, and Palis gave a complete topological invariant distinguishing these dynamical systems. Just this short communication raises several new, and compelling questions for me. S. Lopez de Medrano touched on this point in passing during a beautiful expository lecture, but the setting for the conference provided a wonderful opportunity to learn more.. (3) Mike Davis developed features of local systems in the group algebra of certain discrete groups given by the fundamental group of certain moment-angle complexes. After talking with Mike, the question of whether one can develop 'parametrized macs' arising from representations of their fundamental group looks quite interesting. (4) These 'accidental' contacts have had an impact on my own research which would have not occurred had this conference not been held. I for one found the conference and contact with the participants to be very stimulating, and informative. That BIRS is willing to support such activities is a wonderful contribution to the subject !

Mathematics, University of Rochester

The meeting gave the participants a unique opportunity to meet and discuss with colleagues problems that were being studied in several different areas which included Commutative algebra, algebraic geometry, Combinatorics, dynamical systems, Mathematical Physics, symplectic topology, and algebraic and differential topology.This opportunity will undoubtedly was ideal to start collaborations, I am very optimistic that this will happen soon. The facilities were superb and I want to commend Brenda for her work.

This was a very successful workshop for me ... the workshop had a fantastic impact on my current research by promoting my new result and by giving me a fresh insight and new directions to my future research. I definitely established new contact with few researchers which I wanted to meet in last several years. The workshop just confirmed that Toric Topology is a hot research area with active and successful future.

School of Mathematics, University of Manchester

1) I had the opportunity to interact with Eduardo Gonzalez, who is working on orbifold toric varieties from the point of view of computations in quantum cohomology. This conversation substantially impacts a current project I have on orbifold toric varieties. 2) I also found useful several conversations with Alejandro Adem concerning twisted orbifold Chen-Ruan cohomology, a topic relevant for my joint work with Derek Krepski, another BIRS workshop participant. 3) My postdoc Derek Krepski (mentioned above) was able to meet a large number of researchers working in this area. This will be important when he goes on the job market next academic year (fall 2011). 4) I had several useful conversations with Susan Tolman and Tom Braden which keeps me abreast of developments in their respective research areas.

I experienced fruitful and stimulating discussions with mathematicians from many countries. During the conference, I met many friends and learned their idea in their fields. I found some problem which will be extended to write a paper. In usual conferences, we have chance to communicate only in the lecture hall. But this time, I had chance to discuss mathematics even when we eat meals ... I like the lounge in the Corbett Hall. Every night, I learned many mathematics from people there.

Mathematics, University of the Ryukyus

During the workshop I had the opportunity to meet some of the top researchers in my field of research or closely related fields. I also had the chance to meet some of my collaborators. This had very good impact on my current research. Definitely it motivated some new ideas, research and possibility for some future collaborations and papers.

The BIRS conference on "Integrable and stochastic Laplacian growth in modern mathematical physics" had many impressive talks. My personal interests are in the connections of the Laplacian growth to normal random matrices, and at the talks and discussions during the conference I got new essential information about the normal random matrices. This stimulated my new research project, in which I'd like to develop the Riemann-Hilbert approach to normal random matrices with general polynomial interaction. On a different note, my talk on "Topological expansion in the cubic random matrix model" generated a lively discussion immediately after the talk and later, and this discussion was very interesting and important to me. Finally, there were many good review talks which enhanced my mathematical education.

Mathematical Sciences, Indiana University - Purdue University at Indianapolis

I am a graduate student in my graduating year. I have attended many conferences, and my experience at BIRS was the best, partly because of the participants and organizers, but also because of the accommodation and location of BIRS. The dorm room, facilities, food, service, and other accommodation were excellent. The common area supplied with markers and boards and coffee/tea made for a social environment leading to extensive discussions and lively interactions. I had multiple discussions that sparked new research directions. I was able to meet a postdoc at one of the places I have applied. We had many useful discussions. My interactions influenced some of my other decisions for my job applications as well.

The workshop greatly impacted my research. I am writing a paper on the subject I talked and discussed with participants. I got a new proof of a theorem after the workshop. It is indeed my great pleasure that I could contact with young researchers.

Mathematics, Tokyo Metropolitan University

It was the best workshop I have participated in. The subject is extremely interesting and participants looked at it from different angles. I met people I knew previously by their publications only and also met young researchers I have never heard of but who already obtained some interesting results in the area. Hopefully the workshop will lead to new collaborations and joint papers as a result. I am very grateful to BIRS and the organizers for the opportunity to learn about new interesting directions related to the study of Laplacian Growth.

Mathematics, Ohio University

It was my very first time at BIRS and I enjoyed it very much. I was surprised how easy it is to get to from Europe. Together with Andrea Walther, Angela Kunoth, and Bob Russell, we have submitted a proposal for a workshop on Multiscale Methods and Algorithmic Differentiation ... Larry, Stephen, and Volker did a great job at organizing the workshop.

Indeed, the workshop gave me a lot of good ideas for future research. In particular the interdisciplinary character of the workshop was extremely enlightening. I am sure the same is true for all the young people that were there, who got a lot of inspiration.

This was a very high quality workshop! It did help me reconnect with a number of people I knew plus establish new collaborations. I have a number of exciting new collaborations going forward.

Computer Science, University of Saskatchewan

This was a very interesting workshop for me. I found the scientific contents of workshop well balanced to cover different aspects of differential-algebraic systems (DAEs). In spite of DAE focus, I was pleasantly surprised of the many facets this field could exhibit and how interdisciplinary results in different fields of DAEs could shed a new light to my own work.

Institute of Robotics & Mechatronics, German Aerospace Center

I really engaged in this workshop. Thanks to Dr.Bosh, Dr.Braun and Dr.Bourlioux. My interest was inspired by some of the speakers, which is the goal of joining of this workshop.

The workshop was an occasion to start discussions with colleagues that should result in new collaboration. These discussions provided me with new insight on at least two topics of central interest to my investigations, namely orthogonal polynomials in the plane and rational approximation. Besides, new advances in the field of pluripotential theory and energy discretization were presented in a series of talks that strongly interested me, and will almost certainly influence my research. Altogether, the meeting was very fruitful as far as I am concerned.

One of the fascinating sides of this conference was the diversity and the great quality of the talks (thanks to all participants!). There were several groups working on different aspects of orthogonal polynomials leading to interesting interactions. I believe everyone could see and learn something new; meet old and new friends. I personally had discussions with quite a few of the participants and this will definitely have an impact on my short and long term research plans. ... I would like to thank the staff at BIRS for the superb organization and working conditions! It is much easier to organize a conference with this team on your side! This was my first conference at Banff and I was impressed with the facilities and the setting.

I had a very good time in Banff, which is nothing new. I have always enjoyed my visits to BIRS and I wish BIRS continued success. Specifically to the current program, I enjoyed many of the lectures and had extended discussions with Eric Rains and Yan Xu. I had a three hour meeting with Rains and it was most productive and mutually beneficial. It will lead to some new research work. I also discussed possible research collaboration with Plamen Illiev and Jacob Christiansen. The conference was very successful.

Mathematics, City University of Hong Kong and King Saud University

I was very pleased to be able to participate at the BIRS workshop. In addition to meeting old friends and colleagues, I also learned about new important developments. Of particular interest is the new development of pluripotential theoretic methods in several complex variables that I was not previously aware of. The workshop was extremely stimulating.

As always, BIRS provided a very nice setting for our meeting. And, as usual, the most beneficial aspect for me were some small group discussions outside of the lectures. At least one specific research question I had was solved (not by me!), and several other questions were presented to me for the first time. The talks themselves I found to be of a rather uneven quality, some good, some not so good; but this is likely more to my ignorance of many facets of the material. All in all, I found the conference to be very useful.

The workshop was interesting and well organized. Conditions could hardly have been better.

It was a very useful meeting - because both univariate and multivariate people were together, which is unusual. I learnt a lot, especially about pluripotential theory.

School of Mathematics, Georgia Institute of Technology

From a scientific point of view, this time was very great to me. The level of the talks was very impressive with top speakers who presented their last contributions and contribute with discussions in our "free moments" to continue our learning. On the other hand, the work done by the organizers (T. Bloom, J. S. Geronimo, P. Iliev, D. Lubinsky and E. B. Saff) must be pointed out by their precision. The atmosphere was very friendly as well as the facilities of the BIRS. This was my third stay in BIRS in the last 7 years and I can send you my congratulations for your support.

This was a good workshop with a lot of interaction and excellent talks.

Mathematics, University of Szeged and University of South Florida

The BIRS workshop I attended was quite helpful since I met well known experts in the field who gave talks on their recent work, but even more important was to meet younger researchers and to see what they are doing. I was helpful to them because I could explain that some of their work is related to work that has been done before, but it was interesting to see that they were able to move on from where others stopped in the past. I invited some of the postdocs to visit my university and this may result in new collaboration or even a visiting position for some of them. Meeting some of my collaborators certainly was helpful for my ongoing work with them and some new open problems have been mentioned, which may lead to (joint) papers. At least one paper will result from my visit, since I intend to prepare a paper about the talk I gave, taking into account some of the comments of the other participants.

I benefited a lot from attending this conference. The circumstance provided by Banff centre was pleasant. In the lectures given by the experts and during the informal discussions with them, I learned many new results and fresh insights in the area of orthogonal polynomials. I went to Banff with a blank notebook, and I come back with plenty of interesting problems. In a word, this workshop is very helpful to my future research.

I learnt a lot of new mathematics by attending the many interesting talks during the conference. Also, it was great to have the evenings to speak to experts who are working in similar areas. In fact, my current collaboration project started because I had the time to speak to someone who's based in Europe.

Mathematics, Georgia Tech

This is an excellent workshop: well organized, diverse, high quality talks. I learnt several new things, exchanged ideas with several old friends and colleagues, and renewed my acquaintance with several other people. All in all, a very positive experience and a loud Thank You to the organizers to BIRS.

The workshop was fantastic and I was able to have the opportunity to present/communicate/discuss some of my current research with several paticipants. In particular I got some fresh insights from those discussions on my project "Feichtinger's conjecture for group frames".

Mathematics, University of Central Florida

One of the many things that this workshop did for me, was that it opened up my eyes for the very interesting Kadison-Singer problem. I found it very intriguing and hope to be able to approach this area of research in the future!

Department of Mathematical Sciences, University of Copenhagen

Yes, it impacted my research. I also made some new contacts with whom I may start a collaboration. It also enabled me to connect some of my work with some other work that I did not see as being connected.

This was an excellent workshop, that resulted in several specific ideas and directions for new research. It was one on the best meetings I've attended.

The workshop was certainly great, very well organized, and I enjoyed having great conversations with the organizers and other participants. I have certainly got new ideas after this workshop, and I will acknowledge BIRS in my next future publications as one important source of inspiration in my work. ... looking forward to visiting BIRS in the near future!

My postdoc had an opportunity to present her work to an exceedingly engaged audience - she got what must have been 30 questions in a 30 minute talk, and walked away with a page of ideas for next steps. That would have been worth the trip alone. Also, my graduate student received an immersion in mathematical neuroscience with a net value equal to many months of reading, in 5 days alone. Overall, the meeting was certainly the best week of science I can remember - controversies at the interface of computation, theory, and experiment were debated with an openness that would be hard to realize in any standard setting I've experienced in my career. The result is - as for many participants, I am sure - a long list of ideas to pursue, and new connections. As soon as I finish this testimonial, I am going to move along with two new collaborations myself, both focussing on the role of instabilities and near-instabilities (criticality) in neural networks, both started at Banff.

Through the BIRS workshop I was able to gain a new set of contacts that are extremely likely to lead to collaborative research efforts and grant applications. It also gave me new insight into possible research directions and helped me understand the field from a much broader perspective.

This was most probably the best workshop I ever attended. I was able to meet colleagues with similar interests and, due to the accommodation at BIRS, had the opportunity to have many interesting discussions during the workshop as well as during outside activities.

Tufts University

It was my first visit to BIRS and I thoroughly enjoyed it. It is a beautiful place which is run by friendly staff very efficiently. The restaurant with its excellent food provides a very cozy place for informal chat. The workshop was very stimulating - it was good to get to know researchers who I would not otherwise meet at other conferences. It was a very good idea to have a small group of people and to focus on a specific theme. The workshop really widened my horizon and is very helpful to my research.

My participation in the BIRS workshop impacted my current research and made me aware of new results in my field and related fields.

These are exactly the sorts of meetings I go to nowadays, small, well organized so that there is a viable cross section of participants present. Viable means that the knowledge and interests distances between participants are not too large so that we all learn new things and at the same time can talk to each other in some depth. At the BIRS meeting last week, I learned several new things which I am beginning to think about in more detail. I would strongly recommend that a majority of talks are given via white or blackboard. Power point presentations suffer for two reasons. First, because of all the pretty pictures and professional formatting, one undergoes the illusion that one is understanding more than one actually is. Second, a good blackboard talk allows the listener to peruse the blackboard and be reminded of steps already taken, which steps have already been long passed by the power point flyby. Power point is useful for some slides but, for the kind of meetings that BIRS prides itself on, blackboard discussions should be encouraged. Folk learn far more. ... Thanks to BIRS and the organizers for a wonderful week...

I got together over coffee with one of the participants, with whom I've never collaborated before, and figured out that we can substantially generalize a result he had presented from a recent paper. I expect this to become a new joint paper. Aside from that, I heard some very interesting talks which gave me some interesting ideas. I furthermore received very positive feedback on the talk I had presented, with several participants suggesting various follow-up problems, other angles and connections with other problems I had not considered, which can certainly start new research projects. So all in all, I was very pleased with the workshop, and I certainly hope and look forward to participating in future workshops at BIRS again.

...BIRS workshop "Classification of amenable C*-algebras" has allowed me to meet leading researchers on my field of interest and to exchange interesting ideas with them. I would like to thank BIRS and the organizers for putting together the workshop and inviting me...

The workshop exposed its participants to the newest developments in a relatively long-standing direction of research. I have not previously been active myself in this area, but I perceived clearly that breakthroughs are happening at the moment. I certainly got fresh insight into the nature of certain questions and in particular how to answer them, and I've gotten inspiration to look into problems related to my research.

The workshop is fantastic and stimulating. Got some new ideas, and hope they will lead to new results. There might be new collaborations, although it is still in a very early stage.

I think the program was really excellent. This subject is continuing in a very lively fashion and there were lots of stimulating talks from the world experts. I was also impressed by both the number and quality of talks by young people. I can't answer part two from my own experience, but I think this must have had a very positive effect for young people.

The workshop impacts my personal research a lot. I met several people whose important and interesting papers I had read before but never personally met. I made many new contacts and will pursue my research in the classification of amenable C*-algebras.

I found the workshop very interesting: it was devoted to certain phenomena that are occurring in recent research in the area, and it was presenting these phenomena from different point of views. The scientific program was chosen very carefully and the talks generally were of high level. I was learning some new results that are related to my current research and that might have an impact on my work. The workshop was also a good occasion to intensify some contacts and to learn about some new research activities.

I would like to say that I enjoyed very much the scientific program of this workshop. I am very much impressed by several talks. More precisely, my recent research is about weighted projective lines and Frobenius categories. I learned from the workshop that there are considerable link between my research and various other topics, like noncommutative algebraic geometry, fractionally Calabi-Yau algebras and Kerner's exotic spaces. In the near future, I will study more closely on these topics. In fact, I plan to have some mini-seminar in China, on reading some papers by some participants in this workshop.

Department of Mathematics, University of Science and Technology of China

At this workshop, I met Atsushi Takahashi. During the workshop, we were able to finish a major revision of our paper "Strange duality of weighted homogeneous polynomials" according to the comments of a referee of the journal where we had submitted the manuscript. We got the opportunity to present the results of this paper in two talks and we obtained interesting feedback. We also discussed about an ongoing further research project. One of the main themes of the workshop were relations of the representation theory of finite dimensional algebras with singularity theory and algebraic geometry. My own expertise is in singularity theory, but since the last workshop at BIRS which I attended in 2008 (08w5060), I have been particularly interested in these connections. During the workshop, I have learned a lot about new developments and results in this direction and I have again got many new ideas from the talks and from discussions with other participants. In particular, one subject which attracted my attention were fractional Calabi-Yau categories and I have the feeling that there might be some connection with my current research. Summarizing, the workshop was very useful and stimulating for me and will have impact on my future research.

The Workshop was very stimulating. In particular, the connection between algebra and geometry is very modern and leads to new insights. The selection of talks was perfect and the organizers did a very good job. So I hope we will have another workshop of this kind in two or three years. For my own work I got several ideas, I had many discussions with other participants and I certainly would like to come again.

Mathematisches Institut, University Mï¿½nster

This was the most stimulating meeting I have been to for some time. I came away with new insights and ideas for new projects. The workshop made me realize how important it is to consider non-noetherian graded algebras of exponential growth as homogeneous coordinate rings of non-commutative varieties. I gained a greater appreciation of the work of Minamoto & Mori. I appreciated better the various definitions of the pre-projective algebra and how they give very different perspectives. I realized the significance of abelian categories having no simple objects -- I had previously thought they were somewhat bizarre (with the exception of those arising in Polishchuk's work & those that are hearts (related to irrational slopes) of D^b(coh X) for curves of genus >0. I also appreciated the perspective given by considering sequences of algebras. The workshop will impact my future work (the grant application I am now preparing) and the sorts of problems I will give to my newest graduate students. Great meeting!

Mathematics, University of Washington

I started a new research project in graph theory because of this workshop, on the study of extremal problems for graph immersions. I have a few initial results using both probabilistic methods and graph coloring methods, and the topic is very interesting. The BIRS workshop allowed for collaboration with several people I would not have otherwise worked with. This may lead to a publication. It allowed me to branch off into interesting topics in graph theory that I don't usually think about.

Department of Mathematics, Massachusetts Institute of Technology

I benefited much from this particular workshop. Two highlights for me were the following: 1) I had the chance to give a talk at the workshop, and received some very interesting comments on the material I presented. After some discussion with other participants, it turned out that one of my results could be extended to a more general setting. 2) I met another participant which was interested in the open problems I mentioned in my talk. We had the opportunity to discuss the subject in some length, and eventually decided to start a collaboration on that subject. Besides that, I greatly appreciated the various talks, which in general were of very good quality.

... I liked and enjoyed the conference a lot. I learned new outstanding results, and talked with great people. It looks that it helped me to advance in at least two problems: one of them is about complete minors of small graphs, and the other is about packing of hypergraphs. It is maybe to early to say how the research on these problems will unfold, but I think that important steps ahead were made during the conference. Also it turned out that some my old results are not that bad ... thank you again for the invitation to such a great place!

Very nice experience and interesting workshop, leading to fresh insight on the Mathematics of Rate-independent Systems, new scientific contacts and possible new collaborations.

Structural Mechanics, University of Pavia

The BIRS workshop was one of the best I have ever attended to!!

Mathematics, Universita` di Brescia

Attending the workshop on extremes in climate and weather was important for me and my Ph.D. student for many reasons. We met people that are leaders in the field of extremes in climate and weather, got a good overview of the current status of the field and great ideas to work with. My Ph.D. student is now more motivated to work on his thesis and it is not like he wasnâ€˜t motivated before. The Banff Centre campus creates a great atmosphere for ideas and exchanging ideas. The nearby area allows one to experience nature at itâ€˜s very best. We had a great time at BIRS and in Banff both in terms of scientific work and in terms of enjoying ourself as individuals. Thanks to the staff at BIRS and the Banff Centre.

This was a great workshop where the format was excellently chosen. Not the traditional meeting where you only go to listen to conference talks and then talk to people afterwards. Peter Guttorp made us be highly involved and active in group or on one-to-one discussions. The workshop provide to me many 'fresh insights' on my current work in the area and lots of feedback. It was really interesting to have statisticians and climate experts involved in this workshop and bringing their perspectives together. It was also great to hear about the state of the art in 'climate modeling' and 'extremes' I learn a lot from it and I frankly believe this was one of the most productive meetings I ever attended!

The BIRS workshop was absolutely invaluable for my research. Just to have a chance to converse with so many distinguished statisticians was a one-in-a-lifetime event. I obtained new insights, found out things that I was doing incorrectly (and correctly) and I am certain that I will be using what I have learned in my next papers. Thanks very much for inviting me.

University of Saskatchewan, Centre for Hydrology

Indeed my BIRS visit did help. Two ways: 1) Interaction with other investigators gave me a much clearer view of where I'd like to take my own research agenda in this area; 2) I began two new collaborations with other workshop participants. SO, the workshop was great for me scientifically, as well as a delightful experience all around. My thanks to the BIRS and Banff Center staff and leadership.

The Multivariate Operator Theory workshop helped me find a better perspective toward my own research and that of my student by exposing me to the connections and different points of view from other closely related research currently being pursued by other experts in this area. I felt right at home with just about all of the talks and I feel that the workshop brought me up to the cutting edge of what is going on in this area. The informal discussions outside the lectures (during the regularly scheduled coffee breaks and over the many meals served up by the Institute) were also very valuable.

Department of Mathematics, Virginia Tech

It was a great experience in Banff. The lectures were very good and motivating enough to make you think about pursuing your future research in various fields. This workshop gave me the chance to meet the stalwarts in this field. The people were very encouraging and talking to them were really stimulating. The workshop gives us a fresh insight to the subject and also a view towards current mode of research.

I found BIRS a wonderful place to visit. I learned a lot while I was there, and was able to share ideas and visions of where we could go. I found the scientific dialogue richer than at a normal conference, and I think the surroundings and facilities contributed to it. It is beautiful, you are taken care of, there are no distractions - we could just think about mathematics.

Mathematics, Washington U

Indeed, my visit to BIRS was useful and stimulating. The organizers did an excellent job, they succeeded to make a program which satisfied most of the participants. And we all benefited of the location and the superb conditions offered by BIRS. My discussions with other participants concerning the subject of my talk will certainly help me to improve and continue my research. I also appreciated the permanent presence of Brenda, who solved quickly and efficiently our small administrative problems.

Through the BIRS workshop I attended, I was able to meet Peter Hydon from the University of Surrey in England for the first time. His talk was directly connected with recent research at UBC. I was also to make further connections with developers of MAPLE software (DE solvers) which is connected with current research activity with PDF Raouf Dridi at UBC. Greg Reid is to be commended for the excellent way in which he led and organized the workshop.

Department of Mathematics, University of British Columbia

The workshop was excellent, with so many interesting and nice talks. I found it very helpful to my current work. The organizers had done a great job.

Department of Mathematics and Statistics, University of Calgary

The workshop was very useful to think about new projects and to meet other people of scientific interests close to mine. Indeed, there is a number of people I talked to, and there are perspectives to develop concrete research projects. It was interesting especially to see nice interactions of geometry and partial differential equations. Certainly, I will involve in these projects some of my students and post-docs.

This recent workshop concerning interactions between Allen-Cahn equations, the mathematics around the De Giorgi conjecture, and the geometry of minimal and CMC surfaces, was an unusually good one. The connections between these fields have been known for quite a while, but significant interactions between the rather disjoint groups of analysts and geometers who work on these problems has only occurred quite recently. In my opinion, this workshop was extremely helpful in furthering these interactions. I met several significant people with whom I had not had contact before, and got a LOT of new ideas for my research, started some new projects, and altogether felt that the week was extremely inspiring. I think BIRS is a very good place for meetings and am always very happy to go there, but this one stood out amongst all the meetings I had been to there!

Mathematics, Stanford University

I found the workshop very stimulating and interesting. The environment and Also the banff centre constituted a wonderful place where to work and discuss. The people of BIRS were kind and efficient.

Dipartimento di Scienze Matematiche, Universita' Politecnica delle Marche

The conference was very well-organized. I benefited from it in the following ways: (i) I learned the state of art of the research area; this will help me finding research problems, especially for my Ph.D students. (ii) I got the chance to meet and talk to some of the experts who can shed light on the problem that I am currently working on. This may lead to future collaborations. (iii) I got the chance to make my own research results known to a group of first rate analysts, which helps to disseminate the information.

I truly enjoyed the workshop. I had the opportunity to meet colleagues and discuss joint research with them, as well as meet new people in my community and learn about their research interests. I was also enriched by the workshop program which contained many good talks in diverse areas in computational complexity. This allowed me to learn the current state of the art in areas like hardness of approximation, constraint satisfaction problems, pseudorandomness, work in coding theory which relates to computational complexity and communication complexity.

I learned about recent developments in my field and near by areas. I started two new research projects one of them with a new collaborator. It did not affect my students nor my postdocs but it made me more familiar with the works of some junior researchers. I find the workshop very important as it brings top researchers as well as young ones together and give them the opportunity to deeply discuss new developments and embark on new projects. The Banff workshop (this is the 2nd time I'm participating in a complexity related meeting) is perhaps the best place in the world for discussing complexity theory!

Computer Science, Technion - Israel Institute of Technology

The workshop was excellent! It was a long travel for me (I was coming from and returning to Europe) but I'm really happy I participated.

BIRS was my idea of mathematical heaven. Beautiful surroundings, plenty of time to think, and brilliant colleagues with whom to discuss my ideas.

mathematics department, University of Kentucky

This workshop brought together and facilitated discussions between harmonic and complex analysts and experts in geometric measure theory. This was a great initiative, since harmonic analysis, geometric measure theory and complex analysis (of a single variable) have traditionally and effectively worked in a harmonious fashion. The situation is very different when looking at a similar mix but with complex analysis of a single variable replaced by several complex variables. The workshop provided me with an opportunity to present to and discuss with leaders in the field how recent advances in harmonic analysis and geometric measure theory can impact and lead to a qualitative upgrade in the study of several complex variables, particularly for those aspects that make use of singular integral operators. This is a new direction which has been very little explored and where there is a great deal of work to be done. I regard the workshop as an important step in facilitating collaborations across these fields with the goal of closing the gap between what has been done in the case of a single complex variable and that of several complex variables. This is my second visit to BIRS and I have to say that (even though it may sound cliche) this is indeed a place which inspires creativity! I got again a lot of work done (made substantial progress on a research project and the corresponding paper on the workshop topic), and I had the opportunity to discuss about a future collaborative effort with one of the harmonic analysts in the audience. I also got to know some of the junior people in these fields and learn about their work. I think it is to soon to talk about job prospects and hiring decisions, but I am certainly going to pursue some of the junior people at the workshop to visit and give lectures at the relevant seminars, conferences I will be organizing in the near future.

Many thanks again for the support BIRS has given us in pursuing our research. The BIRS centre is a wonderful research environment.

My visit to BIRS last week was extremely productive. Besides learning the most recent developments from many interesting lectures and discussions, I came up with a few key ideas, during my stay (and on the way to Banff), which solved the problem I have been working on in the last six months. The problem, which has been open for a while, concerns the uniform bounds for gradients of solutions to elliptic equations with highly oscillatory coefficients and Neumann boundary conditions. The results will be published in a joint paper with Carlos Kenig and Fanghua Lin. I am very grateful to the BIRS for its support of my visit.

Colleagues at the workshop had some excellent ideas about how to handle bias in next-generation sequencing data, particularly with regard to read mappability and the effects of sequence features (e.g., GC content). These ideas, and software that is being developed, will have a huge impact on sequencing projects in our Bioinformatics Core facility and various collaborations.

As with my participation in earlier incarnations of this workshop the experience proved invaluable. Firstly, with regard to my own work, the questions and suggestions received, both during and beyond my presentation, have served to re-focus some issues, expand scope of applications, and sharpen the theoretical underpinnings. Secondly, I learned of techniques that were described by other speakers that will have immediate impact on both my methodologic and applied work. Thirdly, and perhaps most importantly, I made some new connections that, while in their infancy, have triggered new and promising collaborations. It is my opinion that the scale and setting of BIRS workshops makes for an ideal breeding ground for fomenting new research and I'm truly appreciative of all the effort that BIRS has invested in enabling this wonderful forum.

The workshop provided a high level overview of what the experts were currently thinking and working on. The ideas on profile likelihoods were very valuable. I will be going back to the talks on the website many times in the next few months. I am hopeful that some work (and a paper) on negative weights will result.

The workshop was excellent and strongly impacted and will impact my current research. My current research is the search for dark matter via indirect detection using the Fermi gamma ray space telescope. The attendees of the meeting were not the usual scientists that I would interact with, and their focus on statistics of discovery made for a very special and unusual conference. This conference peaked my interest in Bayesian statistics, and probably will lead to a graduate course that I will teach on the subject this Fall. I am sure I will understand the subject much better after teaching it to our KIPAC graduate students.

KIPAC, SLAC, Stanford University

I had a very stimulating week at the meeting. BIRS is an excellent venue for workshops of this scale which are, in my opinion, the most fruitful scientific meetings I attend.

Many thanks for hosting an extremely productive workshop in an exceptionally beautiful and stimulating environment. The generosity and hospitality of BIRS has been outstanding. My colleagues Eilam Gross, Ofer Vitells, Kyle Cranmer and I had just completed a paper on the application of asymptotic distributions likelihood ratio statistics for discoveries at the LHC, and the workshop was the perfect venue to present the work and get important feedback. The other contributions as well were very interesting and of direct benefit to the efforts at the LHC to prepare for new discoveries.

This was my second time at BIRS, and both times have been very productive and enjoyable. On this trip, I started two new collaborative projects that I expect to bear fruit in the coming years. I also sat down with a participant who showed me how to prove a conjecture that I had made at the conference! So not only did it inspire creativity, BIRS catalyzed real scientific results.

This was a superb workshop for me. I work directly in this business and we have many high-stakes results being produced at the Tevatron as it collects more data than ever before, opening up our sensitivity to processes we have not been able to test before. It's always a pleasure to talk with people at the LHC who are preparing to confront their data and models with statistical techniques. We have in the past and will continue to learn from each other. It's also quite a pleasure to talk with statisticians on the subject. Some things we are getting consensus on (I think we are settling on a consistent handling of the look-elsewhere effect, for example), and there are other open problems which may not be statistical in nature but which require us to do more work. The organization was outstanding, and the staff very cheerful and helpful.

... thanks to Wynne, to Brenda and Brent and anyone else responsible for what our participants all tell me was a great workshop on statistical issues in discovery claims in particle and astrophysics. The atmosphere produced wonderful vigorous interactions between the three groups and we are all grateful for the opportunity and for the way we were looked after all the way along.

This was an excellent week, both providing fresh insights into an area I am already familiar with and completely different perspectives from the neighbouring astrophysics challenges. The relaxed BIRS atmosphere made for a great environment for informal discussion, which, as usual, was the most important part of the workshop. The single most urgent problem we face, the statistical methods to be used to treat the LHC data, took a big step forward both in a predictable direction (the profile likelihood discussions) and in one I did not foresee (the look elsewhere effect) This second topic greatly benefited from the varied perspectives of the mixed group assembled for the meeting.

Particle Physics, Rutherford Appleton Lab

The meeting on statistical issues pertaining to discovery was one of the most productive meetings I have attended during the past few years. A broad range of ideas were discussed, many of which directly inform my own research in high energy physics. I report briefly on two topics of particular interest to me. I had the opportunity to discuss, with Kyle Cranmer, the implementation of reference priors within the CERN statistical software package RooStats and to sketch out a longer-term project. Reference priors are the cornerstone of a state-of-the-art Bayesian methodology called reference analysis, in which some work by Luc Demortier, Supriya Jain and me was recently completed. Following my discussions with Kyle, I have a much clearer picture of how I should proceed over the next few months. The second topic in which progress was made is that of parton distribution functions (PDFs). Parton distribution functions describe, at a given resolution, the structure of particles such as protons. These functions are a critical input in theoretical predictions of the results of particle collisions at accelerators, such as those occurring now at the Large Hadron Collider (LHC) at CERN. In several discussion with theorists Jon Pumplin and Robert Thorne, a consensus emerged about the utility (indeed, necessity) of performing end-to-end simulations of the statistical methods they use to infer the PDFs from fits to particle collision data. My colleagues recognize that end-to-end simulations are needed if we are to make progress in clarifying currently obscure aspects of their fitting procedures. I regard the launching of a fresh attack on the problem of understanding PDF uncertainties as an important success of the BIRS workshop. There is promise of substantial progress over the next few months. My hope is that Jon and Robert will be able to report as much at the PhyStat 2011 workshop at CERN. This was an enjoyable and productive workshop, made all the more so by the gracious and helpful BIRS staff.

Thanks very much for hosting the Statistical Issues workshop! It provided for a great deal of forward progress on my research area of Parton Distribution Functions. It was particularly useful to have two of the people present (Robert Thorne and myself) who are most involved in the current parton distribution efforts, and who represent different collaborations doing this work, along with a number of high energy physicists,and along with statisticians who were not familiar with this area before the workshop, but who were none-the-less able to quickly grasp the essentials and come up with some new approaches which I am hopeful will turn out to be very productive.

The workshop was very useful for my work as it exposed me to cross-disciplinary issues faced by colleagues in particle physics. I also very much appreciated the opportunity to interact with statisticians. The opportunities for networking and starting up collaborative work were excellent.

Physics Dept, Astrophysics Group, Imperial College London

This was indeed an excellent conference/workshop, well organized, and highly stimulating and useful for me personally. I greatly benefitted from my interaction with many of the speakers and participants (both mathematicians and physicists). No doubt there will be an ongoing dialogue on E8 among many of us as a result of this conference. Wishing you all the best in your efforts to further important mathematical research activities at BIRS.

I learned a lot during the meeting in BIRS and met the world research leaders in the structure of exceptional Lie groups. This was a great workshop.

Last week's meeting was indeed an exciting experience. Apart from meeting the leading experts in the representation and structure theory of Lie groups, it provided a very stimulating atmosphere for discussions between mathematicians and physicists on recent developments concerning the "Great Unification" in the theory of elementary particles.

A big thank you to the organisers for an extremely stimulating workshop, and to BIRS for hosting it, and for encouraging such workshops which cross normal subject boundaries. The three main things I got out of the workshop were: 1. An understanding of why and how theoretical particle physicists are using Lie groups. This was my primary purpose in wanting to attend the workshop in the first place. 2. Meeting Tevian Dray and Corinne Manogue and discussing the different ways we are all using 3 by 3 matrices over octonions, and possible connections between them. This unexpected encounter threw up many interesting ideas which we expect to take further. 3. Working with Kay Magaard on a new algorithm for finding a split Cartan subalgebra in a finite Lie algebra. This algorithm not only has applications to computational study of structure of finite matrix groups in characteristic p, but can also be used to study (especially exceptional) Lie groups over non-algebraically closed fields of characteristic 0.

... thanks for so nice scientific time at BIRS and the conference of Junge,Pisier and Xu was very important for me and not only. The connection of operator space or in words of professor Effros- quantum functional analysis with QIT(quantum information theory) was very important for everybody on that conference. I also find very strong scientific atmosphere during all discussions at talks and later. Thanks also for weather that we can see beautiful Rocky Mountains after talks! Also I find very strong connection with the free probability and random matrices and maybe in future I can also try to make my workshop which I have almost each year in Bedlewo in Poland,sometimes at Banff! This will be great!

I genuinely enjoyed the conference. A top level math conference with internationally known researchers, exciting talks with lots of new results and suggestions for interesting open problems in beautiful surroundings and a great atmosphere.

This specific workshop helped me in many aspects as follows: I found new directions to work on from several talks. I and my coworker improved our result during the workshop. I met many mathematicians, so that I could successfully invite them to my place for the future joint work.

Department of Mathematics, Chungbuk National University

The conference was wonderful. Everything went very smoothly. The choice of speakers left nothing to be desired. And of course, the location is a gem in its own right.

The workshop fit perfectly with my research topics. It allows me to keep in touch with many people from the field. The level was very good according to me.

The workshop was highly stimulating for my research. I learned a lot about the current research in related fields and was able to present my own research and relate it to the work of other people. The main impact of the workshop was to bring together experts in the field of Operator spaces and Quantum Information Theory. This resulted in many new insights. For example, a major conjecture in the field of von Neumann algebras turned out to be of severe importance also in the field of Quantum Information Theory. I consider this to be a conceptual breakthrough. During the workshop I continued the collaboration with various researchers that I did know before. I started new projects and discussed ideas with experts.

This was the third serial workshop that we organized (the previous two being in the CIRM at Luminy, 2007 and 2009). There was a major difference between this workshop and the previous two: its scope was widened to include quantum information. One third of the talks are in QI. This is the first workshop involving these two fields. The interactions between this field with operator spaces/algebras have emerged only since a few years and have proved to be very promising. One good illustration of these interactions is a surprising result obtained by U. Haagerup and M. Musat: as an immediate corollary of their results on the dilation of Markov operators, a subject in operator spaces/algebras, they disproved the famous asymptotic quantum Birkhoff conjecture in QI. This example shows that operator spaces/algebras can provide efficient tools and fresh insights to QI. Conversely, QI can provide many problems to operator spaces/algebras. We firmly believe that this workshop will greatly stimulate the interaction between the two fields and the cooperation between the two communities. A good number of young participants (including fresh PhD and PhD students). One fifth of talks were given by PhD students. This workshop will certainly have an impact on their research. Many new contacts appeared in the workshop, especially those between the participants from the two fields mentioned before. This will impact the development in both fields.

Laboratoire de Mathematiques, Universite de Franche-Comte

Thank you for a great conference on geometric analysis and general relativity! I picked up at least one, maybe two, collaborators at the conference, which will be important for my research. My background is more theoretical, even though I am getting involved in simulations of spiral galaxies. Hence, collaborators with a background in numerics, as I have found at the conference, will be essential to my future progress. I was also able to communicate my new results on dark matter and spiral galaxies to some of the top people in the field, including Prof. Yau from Harvard, Prof. Schoen from Stanford, and Prof. Huisken from the Albert Einstein Institute in Germany. Their feedback and encouragement was wonderful. Also, they will be particularly invaluable as they help disseminate the results presented at the conference by all of the speakers to others around the world. The atmosphere was perfect, and I was very productive in terms of new ideas during the week as well. Time will tell how these ideas pan out. One of my recent Ph.D. graduates, Jeff Jauregui, attended. I can tell that he gained a lot from the experience and has a new perspective on the active areas of research in geometric analysis and general relativity. The organizers deserve a hearty congratulations on an outstanding job! They were successful at getting many of the top people in the world into the same room to exchange and collaborate on ideas. The program they developed was both intensive in terms of talks while also leaving a good amount of time for collaborations and conversations among small groups. Personally, I had so much mathematical fun that it is literally taking me days to recover - that was the maximum intensity that I can muster for one week. The conference was one of my favorites of all time. With three kids at home, I do not travel as much as I used to or would like, so I have become very selective about where I do visit. BIRS is one of the places I intend to go to again and again. Thank you!

The workshop was excellent, the talks of highest quality. I talked with Greg Galloway on a potentially very interesting project on a "Lohkamp-type approach" to the mass-momentum inequality, which we are planning to pursue in the near future. I and Lug Nguyen and Gustav Holzegel had several discussions about an ongoing project concerning the mass of axisymmetric black holes, with some new promising ideas which we plan to explore. Finally, I and Luc Nguyen stayed for another two days after the workshop to continue our collaboration on removable singularites of solutions of stationary Einstein equations. We wrote a first draft of a paper containing the result, which we plan to submit for publication within the next two weeks. We are very grateful to BIRS for the opportunity to work face-to-face on this project.

I have a new PhD student who will be starting on July 1st. His subject will be related to the stability of black strings. It was therefore of great interest to me that at the conference Frans Pretorius reported on his impressive new numerical results on this subject and showed animations which are not otherwise available at this time. What I learned there will definitely influence the project of my student and this talk was the highlight of the meeting for me. It might also interest you to see what I wrote about this on my blog (External link).

This was an excellent workshop. First of all I have to say that the Banff experience is unparalleled. Most of our participants were from Europe and they were most impressed at the high level of support that the station provides, along with the superb facilities (pool and restaurant!) of the Centre, not to mention the local geography. Secondly it’s worth mentioning that the feature that contributed to the success of our workshop more than any other was no doubt the fact that well over half of our sessions were very much discussion-oriented, a constant back-and-forth as we tried to clarify and reinvent the significant outlines of the subject. A perfect venue for such a project.

This workshop was closely connected to my recent research. (I and two of the organizers were the ones who found the connection between Whittaker functions and crystal graphs.) It was valuable to have a workshop which allowed me to meet people working on the crystal graphs side of the subject. I also enjoyed meeting Garland, and we hope to have some conversations this coming year as we are not too distant geographically. These could be very exciting, as a main problem is to find connections between multiple Dirichlet series (MDS) and automorphic objects, and Eisenstein series on loop groups are a strong possibility. And I enjoyed hearing from Diaconu of his latest, very surprising, research, which shows that the topic of endoscopy must enter into the study of even relatively simply MDS which have an infinite group of functional equations.

Department of Mathematics, Boston College

My expertise and main interests only partially overlap with the main subject of the conference. Thus the conference was rather beneficial to me: 1) I gained more insight in the subject. 2) It crystallized (to use that word) some possible future research directions. I liked that the organizers allowed various lengths talks: 30, 45 and 60 minutes.

This was a very stimulating workshop. It was in particular interesting to me since there were many mathematicians from different areas (like number theory, representation theory, physics). It was great to see that the crystal bases I have studied in a different context actually come up in number theory!

I am deeply obliged to ... BIRS for an excellent organization of the workshop: Diophantine Approximation and Analytic Number Theory: A Tribute to Professor Cam Stewart. I enjoyed the workshop very much and learned a lot. It gives me a precious occasion to inspire myself. This workshop is one of the best one among those I have visited to.

I found the meeting both very useful and informative. As an NSF program officer it is nice to sometimes get away and just think about one's own research. This was an excellent facility for doing just that.

The workshop was indeed a great success. For me personally, my research was helped in the following ways: * I was able to continue in person an ongoing collaboration with Karl Dilcher, which will lead to a joint paper being submitted in the next couple of weeks; * I was able to discuss a problem relating to the density of values of n for which u_n is divisible by n with Igor Shparlinski. We have a joint draft paper which needs more 'beef', and we discussed how to do this. In connection with this problem, I also obtained some helpful references from Carl Pomerance on the distribution of pseudoprimes, with which our problem is connected. I also found out from Florian Luca that he has a student working in the same area, so that we have identified another potential collaborator. All-in-all a very helpful week research-wise. (I might add that I am now in Jasper on a side trip, so that my visit has had spinoff benefits ... to the Alberta economy.) Thank you again for the opportunity to visit BIRS.

BIRS has proven to be the envy of research institutes around the world, and I hope that our report will contribute to showing the investors of BIRS that important groundbreaking discoveries are regularly occurring during and subsequent to all BIRS workshops. It is my understanding that the list of such investors includes the Natural Sciences and Engineering Research Council of Canada. With the help of my co-organizers, I am very glad to inform you that the conference met with enormous success, by account of all of the participants, many of whom are regarded as world leaders in their respective research areas. At the time that I submitted my proposal to BIRS, my research programme involved quite a number of research colleagues, evidenced by the number of co-authors I have had in the past few years. Specifically, I was able to use my grant funds to make these connections, and collaborate in a mutually productive manner with quite a number of members of our research community. Since that time, NSERC's new policies regarding the use of grant funds by Adjunct Professors has already, and will continue to have, a devastating impact on my own ability to conduct research, and it is my hope that a more productive approach will result by way of a change to the current restrictions. Despite the above, I will try my best to continue to engage in activities that will hopefully have a positive impact on Mathematics in Canada, one of them being the organization of workshops that bring together world class researchers, young researchers, and also, hopefully, those active researchers who have recently lost their research funding as a result of NSERC's new restrictions.

The discussions at BIRS workshop was very stimulating. I could get to know many important people in the field, and I could introduce our recent results to these people. I was contacted by many people for discussions and possible collaborations. For example, I discussed with Prof. A. Zvelindovsky, with whom I collaborated during the past few years, on further collaborations which reflect the discussions at BIRS workshop. I also discussed with Prof. Z.Y. Sun and Prof. Z.G.Wang for a possible collaborations. I will invite Prof. Sun's student to our lab for a few months for collaboration.

This combination of physics and mathematics has been a great experience. Since the focus of the workshop was very concentrated, this has been one of the most effective meetings that I have attended. The organizers assembled a impressive crowd and I have made several new contacts. Moreover, I intend to write a proposal with one of the participants, which I have met in person for the first time during the meeting.

This was one of the most useful workshops I have attended. There were 13 graduate students, University of Calgary Chair of math and stat, University of British Columbia Chair of graduate studies and graduate secretary, University of Saskatchewan Chair of math and stat and Chair of graduate studies, University of Alberta math and stat Chair and graduate secretary, University of Victoria chair of math and stat, a few other faculty and myself as the Chair of math and cs from the University of Lethbridge in attendance. There was a number of very interesting talks by graduate students in addition to presentations by most of the Chairs. There were talks and discussions on whether graduate students should be given the task of teaching courses. A decision was made to arrange for graduate students from various universities to take courses offered at another university by means of video conferencing. Job hunting tips, teaching graduate courses and concerns about the imbalance between the number of graduate students and the existing open positions were among the interesting topics presented and debated. This was a very well planned and timely Roundtable workshop and must be repeated every year. Thank you very much for your continued invaluable services to mathematics and statistics in Canada and the world.

Math and Computer Science, University of Lethbridge

...the conference at BIRS was very interesting and inspiring for me. For instance, being myself a mathematician on the theoretical side, I found it quite valuable to meet a number of physicists and other applied mathematicians working close to medical and other applications and listen to their talks. Besides, the facilities were excellent. The convenience and standard of the meal service was also excellent, in fact remarkably good. And the location of the institute with the breathtakingly beautiful mountain scenery couldn't be better!

Although not an expert in the topic of Inverse Transport Theory and Tomography, I have learned enough about it to use it in my application area (cloudy atmosphere). Left the workshop with potentially very useful papers to read and connections to pursue. Great venue.

My time at BIRS was the very definition of "time well spent". The monastic setting offered me the unparalleled opportunity to not only meet some of the leaders in the field of inverse theory and tomography (whose papers initiated me into the field years ago) but also to discuss various current problems and ideas with them. I benefited tremendously from several invaluable conversations with some of the giants in my field, and in particular I got the opportunity to discuss new approaches to a problem on geodesic AtRT that has long plagued myself and others. I made a pact with another guest to solve some of the ongoing pesky troubles preventing a direct inversion formula. I should also say it was the highlight of my (very young) career to have been given the opportunity to present our humble research results to such esteemed professionals. It was a resounding success.

...Banff conference was of great importance for me. In addition to the usual (but actually crucial for successful research!) opportunity to find out about the important developments in my field of inverse problems, Banff has given me the opportunity to continue my research collaboration with Profs. M.Lassas and G.Uhlmann and to discuss numerous scientific issues with Profs. A. Nachman and G. Nakamura. I wish success to BIRS which is of so much importance for the advancement of the mathematical research!

Nonlinear Diffusions and Entropy Dissipation: From Geometry to Biology had an impact to my research because it gave me new connections. I had very interesting discussions with S. Ulusoy and D. Kinderlehrer and it is quite possible that this new collaboration will result in a research project and publications.

I indeed wish to express my gratitude towards the organizers of this meeting and BIRS staff. I highly appreciated this week at BIRS: the scientific program was wonderful; most talks were of very high quality, some of them (e.g. the talk by Figalli) were of the highest possible scientific level, and will definitely have an impact on my personal research. I also wanted to say that the style of the meeting (about 20/30 selected participants who spend the whole week together) is from my point of view the best-adapted syle for mathematics (much more efficient than large-scale congresses). Thanks for giving this great opportunity to my colleagues and myself!

This workshop was really special and of very very high level. The selection of speakers and the scheduling of the various days was very well done by the organizers. Very intense discussions. I also enjoyed the view of the Vista dining hall as it was the first time for me since it opened. Outstanding event in an outstanding environment.

I believe this workshop has been an important step in my research career. Some participants have been discussing about starting a new research project in the area of non-linear fractional diffusions, which links some of my current work to the main theme of the workshop. This collaboration would not have been possible without the meeting. It also gave new insight on other diffusion problems I am working in right now.

This workshop provided opportunities to hear of recent developments and meet with collaborators.

My participation in the Western Canada Linear Algebra Meeting that was held at BIRS on May 8-9, 2010 did positively impact my research. Although I did not give a presentation there, I was a co-author on three research presentations, and this gave us valuable feedback on that work. The workshop also enabled me to work with my other collaborators on on-going research projects, one of which was initiated at a BIRS workshop held on February 1-5, 2010. My current graduate student David Grundy and my current post-doc Louis Deaett were both at this workshop, and we all benefited from the interaction with other researchers.

Thank you for letting us have WCLAM at BIRS this past weekend. It was a great success with lots of contributions from graduate students and post-doctoral fellows. The topics covered were fairly broad, from combinatorial matrix theory to numerical analysis to matrix functions. And we just had time to climb Tunnel mountain at lunch time! Peter told participants about the new BIRS funding and everyone there is very happy about this. Congratulations: it is truly a great institution.

Excellent workshop, great organization, really useful conferences. It was a pleasure to see all the colleagues again. The stay at BIRS in the Banff Centre was really nice...

I have twice had the privilege of attending the BIRS workshop on Creative Writing in Mathematics and Science and praise it highly. Having attended many scientific conferences (in the fields of physics and mathematical biology) as well as literary workshops, I can say that the BIRS workshop is special, even unique, both in fostering a community of mathematicians and scientists who are also writers, and providing support for the refinement of our work. My fictional work involves science in two ways. I use characters who are scientists and mathematicians, and I also use ideas and metaphors from math and science to convey the thoughts and emotions of the characters. It has been invaluable to me to get feedback at the BIRS workshop from readers who understand both the science and the literary aims. On the one hand, having scientist/writers respond to my work on a personal level allows for a 'reality check' wrt how I depict the men and women of science/writing. Many mathematicians and scientists who are also artists or writers, especially women, have reported to me that they felt understood by my stories. This is valuable to me because in the broader literary community (where I publish) the two headed science-writer beast is rare and often misunderstood, as are mathematicians and scientists, who, if they appear at all, are generally portrayed in caricature, i.e. more or less as nerdy, crazy, or sociopathic. On the other hand, I have also received invaluable feedback and insights on the science/math material I use in my fiction. For example, I learned about Conway’s free will theorem at this last BIRS meeting, and happened to be working on a section of a novel that discusses free will. In addition, I am deepening my understanding of the arrow of time, also a major theme of my novel, from one of the participants who has researched that area. As in any interdisciplinary field, it is hard to be a jack of all trades, let alone a master, and we rely on the help of sympathetic and informed colleagues. BIRS creative writing in science and mathematics workshop has been masterful in making this a real possibility for me. Thank you for supporting it.

I was grateful for the thoughtful, constructive responses to poems from fellow/sister workshop participants in the Creative Writing in Mathematics and Science Workshop. The broad array of expertise and skills in a variety of scientific content areas and writing genres led to feedback at a very high level, and an atmosphere of humor, appreciation, and support; thank you! I found new directions for my work, solutions to problems in it, and a fascinating variety of new questions and methods to bring to writing! The experience will improve a manuscript that has been a finalist and semifinalist in national contests, and has already suggested a new chapbook to work on; and places to send current work, projects to participate in. My thanks to BIRS, the Banff Centre, Florin & Marjorie, and participants for the stimulating company, the terrific facilities, the great food, the spousal companion policy, the Olympic pool, the glorious mountains!

Waisman Center & Dept. of Communicative Disorders, University of Wisconsin

The workshop "BIRS Creative Writing in Mathematics and Science" was exceptionally appreciated and enjoyed by all participated. Moreover, we connected with the Literary Arts programme at the Banff Centre and organized together the "Breaking Barriers" event, which attracted an unexpectedly large number of participants. Thank you for giving us the opportunity to improve through this wonderful exchange of ideas, which only BIRS could have given to us.

The Creative Writing in Mathematics and Science workshop helped my research immensely. I was able to receive feedback from experts in the mathematical and scientific aspects of my work as well as from experts in associated aesthetic philosophies and methodologies. I have already prepared some pieces for submission (and hopefully publication) based on the editorial feedback I received at the workshop. My research and teaching are located at the intersections between science, mathematics, and creative writing. In addition to the fresh insights I have received in the context of my research, this BIRS workshop has also been an invaluable contribution to my pedagogical thinking. As a direct result of the workshop, I have been exploring ways to reconfigure a graduate course I am designing on the implications for environmental ethics of pataphysics (poetry that imagines itself as math and science). I met many new friends that I plan to continue communicating with about issues related to the workshop. This is a very special and unique gathering. There is nothing else like it that I can think of (I have been working on interconnections between poetry, math, and science for many years). One of the particular highlights this year was the the collaborative event (reading and panel discussion) involving participants from the BIRS workshop and the Literary Arts Writing Program. I really hope these kinds of events will continue in the future and that the BIRS writing workshop will continue to overlap (in terms of dates) with the Writing Studio. This is the second time I have been involved in this particular workshop (my first time was in 2006) and my experiences keep on getting better and more rewarding. I have published works in the past that have emerged from the workshop and I expect I will do so again in future. The work of the organizers this year (Florin Diacu and Marjorie Senechal) was first-rate. I cannot say enough about what a valuable experience this has been for me.

Great workshop, stimulating meetings with creative writers in literature program, have returned home with lots of ideas and homework to do.

I found the workshop on Functional Data Analysis extremely useful and stimulating. The setup of the workshop is different from a typical conference. There is lots of time for discussion and interaction with experts in the field. The environment of BIRS is also superb for such a gathering. I am sure this workshop will have a great impact on my research for the years to come.

I participated in the BIRS workshop in Creative Writing in Mathematics and Science and found the experience extraordinarily helpful to my writing. It was my first serious workshop and I found that it far exceeded my expectations. The discussions were well prepared, thoughtful, wise and considerate. Though my own work was critically evaluated and the suggestions for improvements were extensive and beyond what I had anticipated, I felt a sense of benefit from the discussions. Though tough and critical, the discussions were friendly, without ego jockeying and filled with good humor and benevolent hopes for better writing for all. The organizers did a wonderful job of keeping each session on track and using the time to the benefit of improving the writing of each participant, devoting equal time and commitment to each participant. The discussions were intensely thoughtful and well meaning. Overall, the experience (including hospitality and dining) was far beyond my expectations.

I just sent an email to everyone who participated in this workshop, saying that it was the most insightful, intense and exhilarating workshop that I have ever experienced. As a science writer and poet, it was exactly what I needed at this point in my career... The feedback from everyone was extremely generous and helpful, and I felt very privileged to be part of such a distinguished group of writers and scholars. I have started a new suite of poems based on our discussions (on catastrophe theory). With any luck I will have a draft ms. ready to send to my publisher in the fall. I believe that this kind of interdisciplinary discourse is truly valuable and necessary, not only for individuals like myself but for society as a whole. I congratulate and thank BIRS for supporting this wonderful initiative and I hope it continues.