## Past Members of the Scientific Advisory Board

**Alejandro Adem**(University of British Columbia) - Algebraic Topology, Group Cohomology. Member of BIRS SAB, 2005-2007.**Fred Adler**(University of Utah) - Mathematical Biology**Douglas Arnold**(University of Minnesota) - Numerical Analysis, Partial Differential Equations, Mechanics. Member of BIRS SAB, 2002-2004.**James Arthur**(University of Toronto) - Representation Theory. Member of BIRS SAB, 2001-2003.**Luchezar Avramov**(University of Nebraska) - Commutative Algebra. Member of BIRS SAB, 2008-2010.**Raymundo Bautista**(Universidad Nacional Autonoma de Mexico) - Representation Theory, Lie Theory. Member of BIRS SAB, 2005-2007.**Jean Bellissard**(Westfälisches Wilhelm Universität & Georgia Institute of Technology) - Mathematical Physics. Member of BIRS SAB, 2002-2005.**Jim Berger**(Duke University) - Statistics**Andrea Bertozzi**(University of California Los Angeles) - Nonlinear Partial Differential Equations. Member of the BIRS SAB from 2009-2011.**Karoly Bezdek**(University of Calgary) - Combinatorial, Convex and Discrete Geometry. Member of BIRS SAB, 2005-2007.**Jerry Bona**(University of Illinois at Chicago) - Fluid Mechanics and Partial Differential Equations**Robert Brandenberger**(McGill University) - Theoretical Cosmology**Alex Brudnyi**(University of Calgary) - Applied Mathematics**Jim Bryan**(University of British Columbia) - Algebraic Geometry. Member of BIRS SAB, 2008-2010.**Jennifer Bryan**(University of British Columbia) - Applied Statistics. Member of BIRS SAB, 2012-14.**David Brydges**(University of British Columbia) - Statistical Mechanics. Member of BIRS SAB, 2002-2005.**Andrei Bulatov**(Simon Fraser University) - Theoretical Computer Science**Carlos Castillo Chavez**(Arizona State University) - Epidemiology. Member of BIRS SAB, 2008-2010.**Alice Chang**(Princeton University) - Geometric Analysis. Member of BIRS SAB, 2008-2010.**Jennifer Chayes**(Microsoft Research) - Phase Transitions in Combinatorics and Computer Science, Structural and Dynamical Properties of Self-Engineered Networks, and Auction Algorithms. Member of BIRS SAB, 2001-2004.**Vladimir Chernousov**(University of Alberta) - Algebraic Groups. Member of BIRS SAB, 2005-2007.**Richard Cleve**(University of Waterloo) - Algorithms and Complexity Theory, Quantum Computing, Cryptography. Member of BIRS SAB, 2001-2004.**Ralph Cohen**(Stanford University) - Algebraic/Differential Topology. Member of BIRS SAB, 2008-2010.**Ronald Coifman**(Yale University) - Nonlinear Fourier Analysis, Wavelet Theory, Singular Integrals, Numerical Analysis and Scattering Theory, Real and Complex Analysis, New Mathematical Tools for Efficient Computation and Transcriptions of Physical Data, with Applications to Numerical Analysis, Feature Extraction Recognition and Denoising.Member of BIRS SAB, 2002-2004.**Daniel Coombs**(University of British Columbia) - Mathematical Biology. Member of BIRS SAB from 2008, 2010-11.**Octav Cornea**(Universite de Montreal) - Algebraic/Symplectic Topology. Member of BIRS SAB, 2005-2007.**Jakša Cvitanić**(California Institute of Technology) - Mathematical Finance. Member of the BIRS SAB, 2005-2007.**Henri Darmon**(McGill University) - Algebraic Number Theory, with a special emphasis on Elliptic Curves, Modular Forms, and their Associated L-functions. Member of BIRS SAB, 2001-2003.**Kenneth R. Davidson**(University of Waterloo) - Operator theory, Nonselfadjoint operator algebras, C*-algebras.Member of, BIRS SAB, 2001-2003.**Gerda de Vries**(University of Alberta) - Mathematical Biology. Member of BIRS SAB, 2013-2014.**Charmaine Dean**(Western University) - Statistics**Luc Devroye**(McGill University) - Computer science and Probability Theory**Darrell Duffie**(Stanford University) - Mathematical Economics. Member of BIRS SAB, 2005-2007.**Weinan E**(Princeton University) - Scientific Computing/Applied Mathematics. Member of BIRS SAB, 2007-2008.**David Eisenbud**(Mathematical Sciences Research Institute) - Commutative Algebra, Algebraic Geometry, Computation.Member of BIRS SAB, 2001-2005.**Ivar Ekeland**(Université Paris-Dauphine) - Mathematical Economics. Member of BIRS SAB, 2003-2005.**Yakov Eliashberg**(Stanford University) - Symplectic geometry, Topology, Several Complex Variables. Member of BIRS SAB, 2006-2008.**Lawrence Craig Evans**(University of California, Berkeley) - Nonlinear PDE & Calculus of Variations. Member of BIRS SAB, 2003-2005.**Steve Evans**(University of California, Berkeley) - Probability. Member of BIRS SAB, 2012-2014.**James Feng**(University of British Columbia) - Fluid dynamics, cell and tissue mechanics**Stephen E Fienberg**(Carnegie Mellon University) - Statistics**Daniel Freed**(University of Texas at Austin) - Geometry, Math Physics. Member of BIRS SAB, 2005-2007.**John Friedlander**(University of Toronto) - Number Theory. Member of BIRS SAB, 2003-2005.**Jean-Marc Gambaudo**(Universite de Nice - Sophia Antipolis) - Geometry and Analysis. Member of BIRS SAB, 2007-2009.**Peter Glynn**(Stanford University) - Discrete and stochastic systems in management science and engineering. Member of SAB 2011-2014.**Randy Goebel**(University of Alberta) - Computer science**Xavier Gomez-Mont**(CIMAT) - Dynamical Systems. Member of BIRS SAB, 2008-2010.**Eyal Goren**(McGill University) - Arithmetic Geometry. Member of BIRS SAB, 2006-2008.**Timothy Gowers**(Cambridge University) - Combinatorics. Member of SAB 2011-2014.**Vivek Goyal**(3dim) - Sampling, Quantization, Magnetic Resonance Imaging, and Optical Imaging**Andrew Granville**(Université de Montréal) - Number Theory**Robert Gray**(Stanford University) - Electrical Engineering. Member of BIRS SAB, 2007-2009.**Mark Green**(University of California, Los Angeles) - Algebraic geometry and Commutative Algebra**David Gross**(University of California, Santa Barbara) - Theoretical Physics and String theory. Member of BIRS SAB, 2001-2004.**Arvind Gupta**(University of British Columbia) - Combinatorics, Optimization and Complexity Theory. Member of BIRS SAB, 2001-2005.**Robert Guralnick**(University of Southern California) - Group theory**Peter Guttorp**(Norwegian Computing Center) - Uses of Stochastic Models in Scientific Applications in Hydrology, Atmospheric Science, Geophysics, Environmental Science, and Hematology. Member of BIRS SAB, 2001-2003.**Pavol Hell**(Simon Fraser University) - Computational Combinatorics. Member of BIRS SAB, 2008-2010.**Sheila Hemami**(Cornell University) - Electrical Engineering**Helmut Hofer**(Institute for Advanced Studies) - Symplectic Geometry. Member of BIRS SAB, 2003-2005.**G. M. (Bud) Homsy**(University of California Santa Barbara) - Fluid Mechanics**Gerhard Huisken**(Universitaet Tuebingen) - Analysis and Differential Geometry, Geometric Evolution Equations. Member of BIRS SAB, 2005-2007.**Craig Huneke**(University of Virginia) - Commutative Algebra including Linkage Theory and specific work on Commutative Noetherian Ring R. Algebraic geometry.Member of BIRS SAB, 2001-2004.**Jacques Hurtubise**(McGill University) - Topology and Geometry.Member of BIRS SAB, 2001-2003.**Lisa Jeffrey**(University of Toronto) - Symplectic Geometry. Member of BIRS SAB, 2005-2007.**Bill Johnson**(Texas A&M University) - Geometric Functional Analysis. Member of SAB 2011-14.**Valentine Kabanets**(Simon Fraser University) - Computational Complexity**Niky Kamran**(McGill University) - Differential Geometry. Member of BIRS SAB, 2008-2010.**Yael Karshon**(University of Toronto) - Symplectic Geometry**Svetlana Katok**(The Pennsylvania State University) - Dynamical Systems**Carlos Kenig**(University of Chicago) - Analysis**Nancy Kopell**(Boston University) - PDE and Applied Mathematics including; Mathematical Modeling of Networks of Neurons in Vertebrates and Invertebrates. Member of BIRS SAB, 2001-2004.**Thomas Kurtz**(University of Wisconsin) - Statistics. Member of BIRS SAB, 2005-2007.**Rachel Kuske**(University of British Columbia) - Applied Partial Differential Equations. Member of BIRS SAB, 2005-2007.**Matilde Lalin**(Université de Montrèal) - Number Theory**Kristin Lauter**(Microsoft Research) - Number theory**Robert Lazarsfeld**(Stony Brook University) - Algebraic Geometry. Member of BIRS SAB, 2005-2007.**Randy LeVeque**(University of Washington) - Scientific computing and partial differential equations**Mark Lewis**(University of Alberta) - Mathematical Biology, with a focus in Spatial Ecology. Mathematical models include Nonlinear Partial Differential Equations, Integrodifference Equations and related Stochastic Spatial Processes. Biological problems include modeling the process of territorial pattern formation in wolves, predicting population spread in biological invasions, calculating optimal strategies for biocontrol, and assessing the effect of habitat fragmentation on species survival. Member of BIRS SAB, 2001-2004.**Elon Lindenstrauss**(Hebrew University) - Ergodic Theory. SAB Member 2011-2014.**Laszlo Lovasz**(Eötvös Loránd University)**Michael C. Mackey**(McGill University) - Math Biology. Member of BIRS SAB, 2008-2010.**Jitendra Malik**(University of California, Berkeley) - Computer Vision. Member of BIRS SAB, 2001-2003.**Rafe Mazzeo**(Stanford University) - Geometric and Microlocal Analysis, Partial Differential Equations. Member of BIRS SAB, 2008-2010.**Peter McCullagh**(University of Chicago) - Statistical theory and Applications**Dusa McDuff**(Stony Brook University) - Global Symplectic Geometry. Member of BIRS SAB, 2001-2004.**Robert Moody**(University of Victoria) - Continuous Symmetries and the Theory of Lie groups and Lie Algebras. Member of BIRS SAB, 2001-2003. CHAIR.**David Mumford**(Brown University) - Machine and Natural Intelligence, including Pattern Theory. Member of BIRS SAB, 2001-2003.**Robert Myers**(Perimeter Institute) - General Relativity and String Theory. Member of BIRS SAB, 2001-2004.**Ken Ono**(Emory University) - Number Theory**Hirosi Ooguri**(California Institute of Technology) - Math Physics**Irena Peeva**(Cornell University) - Commutative Algebra**Yuval Peres**(Microsoft Research) - Statistical Mechanics/Probability**Victor Perez-Abreu**(Centro de Investigacion en Matematicas) - Probability and Statistics. Member of BIRS SAB, 2008-2010.**Ed Perkins**(UBC) - Probability.Member of BIRS SAB, 2001-2004.**Arturo Pianzola**(University of Alberta) - Infinite dimensional Lie theory. Member of BIRS SAB, 2008-2009.**Nicholas Pippenger**(Princeton University) - Theoretical Computer Science and Communication Theory and Mathematics. Member of BIRS SAB, 2001-2004.**Gilles Pisier**(Texas A & M University) - Modern Analysis. Member of BIRS SAB, 2008-2010.**Daniel Pollack**(University of Washington) - Differential geometry**Mary Pugh**(University of Toronto) - Applied Partial Differential Equations. Member of BIRS SAB, 2005-2008.**Ian Putnam**(University of Victoria) - Dynamics and Operator Algebras.Member of BIRS SAB, 2001-2003.**Sujatha Ramdorai**(University of British Columbia) - Algebraic K-theory, Algebraic Number theory, Motives, Iwasawa theory. Member of BIRS SAB 2011-2013.**James Ramsay**(McGill University) - Statistics**Alexander Razborov**(University of Chicago) - Combinatorics, Theoretical Computer Science. Member of BIRS SAB, 2005-2008.**Zinovy Reichstein**(University of British Columbia) - Algebra, Algebraic geometry and algebraic groups**Nancy Reid**(University of Toronto) - Statistics**Walter Schachermayer**(University of Vienna) - Math Finance and Economics. Member of BIRS SAB, 2008-2010.**Dominik Schoetzau**(University of British Columbia) - Computational Mathematics, Scientific Computation**José Antonio Seade Kuri**(Universidad Nacional Autonoma de Mexico) - Singularity theory and complex geometry. Member of BIRS SAB, 2011-2014.**Gordon Semenoff**(University of British Columbia) - Particle & Nuclear Physics, Theoretical Physics**Gadiel Seroussi**(MSRI) - Information Theory. Member of BIRS SAB, 2005-2006.**Gordon Slade**(University of British Columbia) - Probability, Statistical Mechanics. Member of BIRS SAB, 2005-2007.**Karen Smith**(University of Michigan) - Commutative Algebras. Member of BIRS SAB, 2005-2007.**Panagiotis Souganidis**(University of Chicago) - Nonlinear Partial Differential Equations. Member of BIRS SAB, 2006-2009.**Douglas Stinson**(University of Waterloo) - Computer Science, Cryptography. Member of BIRS SAB, 2005-2007.**Benny Sudakov**(ETH - Zurich) - Combinatorics**Elizabeth Thompson**(University of Washington) - Statistics. Member of BIRS SAB, 2005-2007.**Gang Tian**(Princeton University) - Geometry: Differential Geometry, Algebraic Geometry, Geometric Analysis and Partial Differential Equations. Member of BIRS SAB, 2001-2004.**Rob Tibshirani**(Stanford University) - Data Mining and Computational Statistics. Member of BIRS SAB, 2001-2003.**Nicole Tomczak-Jaegermann**(University of Alberta) - Asymptotic Geometric Analysis. Member of BIRS SAB, 2005-2007.**Nizar Touzi**(Ecole Polytechnique) - Financial Mathematics**Richard Tsai**(University of Texas at Austin) - Multiscale Modeling and Computations**Gunther Uhlmann**(University of Washington) - Inverse Problems. Member of BIRS SAB, 2008-2010.**Alberto Verjovsky**(UNAM Mexico) - Dynamical systems, geometric topology, theory of real and complex foliations**Jeff Viaclovsky**(University of Wisconsin) - Differential Geometry and Geometric Analysis**Cédric Villani**(l'Institut Henri Poincaré) - Partial Differential Equations**Michael Vogelius**(Rutgers University)**Michael Ward**(University of British Columbia) - Applied Partial Differential Equations and Asymptotic Analysis**Michael Waterman**(University of Southern California) - Mathematical and Computational Biology. Member of BIRS SAB, 2003-2005.**Peter Winkler**(Dartmouth College) - Discrete Mathematics and the Theory of Computing. Member of BIRS SAB, 2003-2005.**Daniel Wise**(McGill University) - Geometric Group Theory and 3-manifolds**Margaret Wright**(New York University) - Optimization, Linear Algebra, Numerical and Scientific Computing, and Scientific and Engineering Applications. Member of BIRS SAB, 2001-2003.**Jianhong Wu**(York Institute for Health Research, York University) - Applied Mathematics, Mathematical Biology. Member of BIRS SAB, 2005-2007.**Shing-Tung Yau**(Harvard University) - Differential Geometry. Member of BIRS SAB 2011-2014.**Efim Zelmanov**(University of California, San Diego) - Algebra, Group Theory, Non-associative Algebras. Member of BIRS SAB, 2003-2005.**James Zidek**(University of British Columbia) - Statistics. Member of BIRS SAB, 2007-2010.

## Bio sketches

**Alejandro Adem**(University of British Columbia)Alejandro Adem is a Professor of Mathematics at UBC. In 1982 he received his BS from the National University of Mexico, and in 1986 he received his Ph.D. from Princeton University, under Bill Browder. After holding a Szego Assistant Professorship at Stanford University and spending a year at the Institute for Advanced Study in Princeton, he joined the faculty of the University of Wisconsin in 1990, and remained there until he joined UBC in 2004. Adem has held visiting positions at the ETH-Zurich, the Max Planck Institute in Bonn, the University of Paris VII and XIII, and most recently at Princeton University. Adem's mathematical interests vary widely over topics in algebraic topology, group cohomology and related areas. He has given over 150 invited lectures, however his toughest assignment was preparing a lecture for the celebrated Bourbaki Seminar in Paris. His monograph "Cohomology of Finite Groups" (jointly written with R. James Milgram) was published as a Springer-Verlag Grundlehren (Volume 309) in 1994, and a second edition appeared in 2005. Adem served as Chair of the Department of Mathematics at UW-Madison during the period 1999-2002. He was awarded an NSF Young Investigator Award in 1992, a Romnes Faculty Fellowship in 1995 and a Vilas Associate Award in 2003. He is an editor for the Transactions of the American Mathematical Society. He is currently co-chair of the Scientific Advisory Committee for the Mathematical Sciences Research Institute in Berkeley. In 2004 Alejandro was appointed Canada Research Chair in Algebraic Topology at UBC, and on January 1, 2005 he became the Deputy Director of PIMS.

**Fred Adler**(University of Utah)Fred Adler received his BA in Mathematics from Harvard in 1984, and a PhD in Applied Mathematics from Cornell University in 1991. After a post-doc at the University of California at Davis, Adler joined the faculty at the University of Utah as a joint appointment in Mathematics and Biology. He investigates many areas of mathematical biology, generally those starting with vowels, including ant biology, ecology, epidemiology, evolution, immunology, infectious diseases, oncology and urban ecology. He is the author of the textbook "Modeling the Dynamics of Life: Calculus and Probability for Life Scientists," now in its third edition with Brooks-Cole Publishing Company, and has co-authored a textbook on urban ecology, "Urban Ecosystems: Ecological Principles for the Built Environment," now in production with Cambridge University Press. Adler was awarded the Distinguished Mentor award by the University of Utah, and was recently elected president of the Society for Mathematical Biology.

**Douglas Arnold**(University of Minnesota)Douglas N. Arnold is Director of the Institute for Mathematics and its Applications and Professor of Mathematics at the University of Minnesota. The primary mission of the IMA is to increase the impact of mathematics by fostering research of a truly interdisciplinary nature, linking mathematics of the highest caliber and important scientific and technological problems from other disciplines and industry. The IMA is a partnership of the National Science Foundation, the University of Minnesota, and a consortium of participating universities, laboratories, and corporations, and represents the largest mathematics research investment of the National Science Foundation. Dr. Arnold's research interests include numerical analysis, partial differential equations, mechanics, and in particular, the interplay between these fields. Much of his work has concerned finite element methods, with the main applications being to the numerical simulation of elastic plates and shells, and also of incompressible fluids. He also works in computational relativity, with the long-term goal of the numerical simulation of massive astrophysical events, such as black hole collisions, and the resulting gravitational radiation emission. Prof. Arnold received his Ph.D. degree in Mathematics from the University of Chicago in 1979. From 1979 through 1989 he was on the faculty of the University of Maryland. In 1989 he moved to Penn State University where he was appointed Distinguished Professor Mathematics, and where he remained until assuming the position of Director at the Institute for Mathematics and its Applications in August 2001. He has written about 75 papers, serves on the editorial boards of numerous journals, and has been designated as a ''Highly Cited Author" by Thomson ISI. In 1991 he was awarded the first International Giovanni Sacchi Landriani Prize by the Academy of Arts and Letters of Lombardy Institute in Milan in 1991 for "outstanding contributions to the field of numerical methods for partial differential equations." In 2002 he was a plenary lecturer at the International Congress of Mathematicians in Beijing. Arnold serves on a variety of advisory and scientific boards, including the Council of the Society of Industrial and Applied Mathematics, the Mathematical and Physical Sciences Advisory Committee of the National Science Foundation, the Advisory Board of DIMACS, and the Scientific Advisory Board of the Norwegian Centre of Mathematics for Applications. At Penn State he was awarded the George W. Atherton Award for Excellence in Teaching by the University in 1996, the Teresa Cohen Service Award by the Mathematics Department in 1998, and the Distinguished Service Award by the Eberly College of Science in 2000. There he also served as co-director of the Center for Computational Mathematics and Applications and as associate director of the Institute for High Performance Computing Applications, and was a member of the Center for Gravitational Physics and Geometry.

**James Arthur**(University of Toronto)Professor James Arthur has published 56 research papers, comprising over two thousand pages in mathematical journals of the highest reputation. He is regarded as one of two or three leading mathematicians in the world in the central fields of representation theory and automorphic forms. In addition to being an outstanding scientist, Professor Arthur is an excellent teacher and has a distinguished record of service to both the University and the mathematics community. Representation theory is the study of the deeper aspects of symmetry. The notion of symmetry plays a prominent role in mathematics, and indeed throughout much of science. It is a fundamental unifying force. Representation theory probes the hidden mathematical properties of symmetry in much the same way that spectroscopy analyzes hidden physical properties of light and matter. Automorphic forms is the branch of representation theory that relates symmetry with arithmetic and number theory. According to a general philosophy of R. Langlands of Princeton, automorphic forms hold the key to unifying vast areas of mathematics, some of which date back several centuries. The Langlands programme is a stunning blueprint for relating arithmetic and algebra on the one hand, with analysis and spectral theory on the other. Over the past thirty years, Professor Arthur has been a leader in the quest to take the Langlands programme from the realm of conjecture to actual mathematical realization. In so doing, he made many fundamental discoveries, which have had a tremendous impact on mathematical research. In a series of papers that spanned two decades, he was able to construct the general trace formula, a mathematical equation of enormous power that had been sought by mathematicians since the 1950s. His joint work with L. Clozel, which appeared in Annals of Mathematics Studies, solved a critical comparison problem for trace formulae on different groups. He has introduced a remarkable conjectural classification of automorphic representations, in terms of what are now known as Arthur packets. In the early 1990s, he found a local version of the trace formula that had been conjectured by D. Kazhdan. Professor Arthur is highly sought after as a lecturer on the international scene. His oral and written exposition of mathematics is clear and inspiring. He is a dedicated mentor of young faculty and graduate students. His active role in the International Mathematical Union, which organizes the International Congress of Mathematicians every four years, has brought Canada to greater prominence on the world mathematical stage. Professor Arthur has achieved many distinctions in his career. Elected as a Fellow of the Royal Society of Canada in 1980 and the Royal Society of London in 1992, he became the first recipient of the Synge Award of the Royal Society of Canada in 1987. He was awarded the CRM/Fields Institute Prize and the Henry Marshall Tory Medal in 1997. In 1999 he received the Canada Gold Medal for Science and Engineering from NSERC, making him the only mathematician to have won Canada's top award in science. Professor Arthur has twice been an invited lecturer for the International Congress of Mathematicians. He was awarded the Wilbur Lucius Cross Medal from the Graduate School of Yale University and a Guggenheim Fellowship in 2000. In 2002, he received an honorary doctorate from the University of Ottawa in recognition of his achievements in mathematics.

**Luchezar Avramov**(University of Nebraska)Luchezar Avramov holds, since 2002, the Dale M. Jensen Chair in Mathematics at the University of Nebraska - Lincoln. His research interests are in commutative algebra and homological algebra, spilling into ring theory, algebraic geometry, and algebraic topology. He earned his Ph.D. from Moscow State University in 1975. Between 1975 and 1990 he was on the faculty of the University of Sofia and the Bulgarian Academy of Sciences. From 1991 through 2001 he was Professor of Mathematics at Purdue University. He has held visiting positions at many institutions, among them: Warwick University (as UNESCO Fellow), Institute Mittag-Leffler, University of Stockholm, University of Paris VI, University of Illinois (as Miller Scholar), University of Toronto, Moscow State University, University of Lille, University of Copenhagen, University of Nice, Meiji University, University of Paris XIII, MSRI, TIFR. He delivered Plenary Addresses at the CMS Summer Meeting in Toronto (1992), the AMS Meeting in Kent (1995), and the 6th International Joint Meeting of the AMS and the SMM in Houston (2004). Avramov currently serves on the editorial boards of the Transactions of the AMS, the Journal of Algebra, the Illinois Journal of Mathematics, and Homology, Homotopy and Applications.

**Raymundo Bautista**(Universidad Nacional Autonoma de Mexico)

**Jean Bellissard**(Westfälisches Wilhelm Universität & Georgia Institute of Technology)Jean Bellissard (http://www.math.gatech.edu/~jeanbel) is Senior Professor at the Westfälische Wilhelms-Universität, Münster, Germany and Emeritus Professor of Mathematics and Professor of Physics at Georgia Institute of Technology. He received his Ph.D from the University of Provence, Marseille, in 1974. His research interests are in Mathematical Physics. Since 1980 he has worked on various applications of Noncommutative Geometry as well as problems in Solid State Physics. He spent twenty years at the University of Provence, Marseille from 1970 till 1990 where he became a Full Professor of Physics in 1986. During this period he stayed at the University of Lausanne as Assistant Professor in 1974-75, at the Princeton University as an Associate Professor in 1983-84 and at the Wissenschaftskolleg zu Berlin as a Fellow in 1990-91. He moved to Toulouse to create a group of Theoretical Physics from 1991 till 2002 and moved to Georgia Tech in August 2002. He retired in June 2017 to move to Germany. Bellissard was awarded the Langevin Prize of the French Physical Society in 1988. He was an invited lecturer at the 1994 ICM in Zurich, He became a Senior Member of the Institut Universitaire de France in 1995-2002. He became a Fellow of the American Mathematical Society in 2013. He has been the Chief Editor of the Annales de l\'Institut Henri Poincare (Theoretical Phyics) from 1993 till 2000 and worked at merging this journal with Helvetica Physica Acta, which became Annales Henri Poincare in 2000. He has also served on the Board of the French Mathematical Society and on the Prize Committee of the French Physical Society. He currently serves on the Editorial Board of Annales Henri Poincare, Review of Mathematical Physics, Electronic Journal of Mathematical Physics, Journal of Noncommutative Geometry, Journal of Fractal Geometry.

**Jim Berger**(Duke University)Jim Berger received a Ph.D. from Cornell University in 1974. He was in the Department of Statistics at Purdue University until 1997, at which time he moved to the Institute of Statistics and Decision Sciences (now the Department of Statistical Science) at Duke University as the Arts and Sciences Professor of Statistics, the position he currently holds. He was the founding director of the Statistical and Applied Mathematical Sciences Institute, a National Science Foundation institute focused on interdisciplinary research involving statistics and mathematics, serving from 2002-2010. Berger was president of the Institute of Mathematical Statistics from 1995-1996, chair of the Section on Bayesian Statistical Science of the American Statistical Association in 1995, and president of the International Society for Bayesian Analysis during 2004. He has been involved with numerous editorial activities, including co-editorship of the Annals of Statistics during the period 1998-2000. He has served on numerous societal, organizational, academic, and governmental councils, committees, panels, and boards, including being chair of the Advisory Committee for the NSF Directorate on Mathematical and Physical Sciences since 2010. Berger is a Fellow of the ASA and the IMS and has received Guggenheim and Sloan Fellowships. He received the Committee of Presidents of Statistical Societies ‘President's Award’ in 1985, and the Sigma Xi Research Award at Purdue University for contribution of the year to science in 1993. He was the COPSS Fisher Lecturer in 2001 and the Wald Lecturer of the IMS in 2007. He was elected as a foreign member of the Spanish Real Academia de Ciencias in 2002, elected to the USA National Academy of Sciences in 2003, was awarded an honorary Doctor of Science degree from Purdue University in 2004, and became an Honorary Professor at East China Normal University in 2011.

**Andrea Bertozzi**(University of California Los Angeles)Andrea Bertozzi is Professor of Mathematics at UCLA and currently serves as Director of the Program in Computational and Applied Mathematics. From 1995-2004 she was on the faculty of Duke University, most recently as Professor of Mathematics and Physics. During 1995-6 she was Maria Goeppert-Mayer Distinguished Scholar at Argonne National Laboratory. From 1991-1995 she was a Dickson Instructor at the University of Chicago. She received AB, MA, and PhD degrees in Mathematics from Princeton University. Her current research interests include image inpainting, image segmentation, cooperative control of robotic vehicles, swarming, and fluid interfaces. Professor Bertozzi has served as a plenary/distinguished lecturer for both SIAM and AMS and is associate editor for approximately ten journals. Her past honors include a Sloan Foundation Research Fellowship and the Presidential Career Award for Scientists and Engineers from the Office of Naval Research. She was awarded SIAM’s Sonia Kovalesky Prize at the 2009 Annual meeting in Denver. She is a fellow of the American Academy of Arts and Sciences, and a fellow of three professional societies: AMS, SIAM and the APS. She is a member of the US National Academy of Sciences. http://www.math.ucla.edu/~bertozzi/

**Karoly Bezdek**(University of Calgary)Karoly Bezdek was born on May 28, 1955 in Budapest Hungary. He is married and has three children. He received his Dr.rer.nat. degree (1980) as well as his Habilitation degree (1997) in mathematics from the Eotvos Lorand University, in Budapest, Hungary and his Candidate of Mathematical Sciences degree (1985) as well as his Doctor of Mathematical Sciences degree (1994) from the Hungarian Academy of Sciences. He worked at the Department of Geometry of Eotvos Lorand University between 1978-2003 and was the chair of the department from 1999 to 2003. During the period 1978-2003 he held several visiting positions at research institutions in Canada, Germany, Holland, and USA including the period of about 7 years at Cornell University in Ithaca, New York. Currently he is the Canada Research Chair (Tier 1) of Computational and Discrete Geometry at the University of Calgary. His field of research is combinatorial, convex and discrete geometry. He is the author of more than 120 research publications including 3 books and is the founding editor-in-chief of the e-journal "Contributions to Discrete Mathematics".

**Jerry Bona**(University of Illinois at Chicago)Jerry Bona received his Ph.D. under the guidance of Garret Birkhoff in 1971. He was a post-doc with Brooke Benjamin at the University of Essex in 1970-72 before joining the department of mathematics at the University of Chicago as an L.E. Dickson instructor. He rose through the ranks, becoming Professor there in 1979. He moved to Penn State to set up a fluid mechanics laboratory in their mathematics department. Later, he joined the mathematics department and the Texas Institute for Computational and Applied Mathematics at the University of Texas at Austin. He is currently professor of mathematics in the Mathematics, Statistics and Computer Science Department at the University of Illinois at Chicago. Bona's research is mainly in fluid mechanics and partial differential equations, but he has also written in oceanography, coastal engineering, numerical analysis, economic theory and biology.

**Robert Brandenberger**(McGill University)Robert Brandenberger is currently Canada Research Chair and Professor of Physics at McGill University. He obtained his undergraduate degree from the ETH in Zurich and his PhD from Harvard University, spent time as a postdoctoral fellow at the Institute for Theoretical Physics at UCSB and at DAMTP (Cambridge University). Before moving to McGill in 2004 he taught at Brown University. He is the winner of the 2011 CAP/CRM Prize in Mathematical Physics. From 2009 to 2011 he was a Killam Research Fellow. His main research interests are in the field of theoretical cosmology.

**Alex Brudnyi**(University of Calgary)Alex Brudnyi received his Ph.D. degree from the Technion, Israel Institute of Technology, in 1995; he was the recipient of the NSERC postdoctoral fellowship and held the postdoctoral position at the University of Toronto (1996-1998). He was awarded the Andre Aisenstadt Mathematics Prize (2002), the Max Plank Institute for Mathematics Research Fellowship (2006) and the NSERC Discovery Accelerator Supplement (2010-2013). His research is mainly in the areas of Function Theory, Geometrical Analysis, Dynamical Systems and Commutative Banach Algebras. He has published more than 75 research papers and two books on Geometric Analysis.

**Jim Bryan**(University of British Columbia)Jim Bryan received his BS from Stanford in 1989 and his PhD at Harvard in 1994. He had postdoctoral fellowships at UC Irvine and UC Berkeley. He joined the faculty at Tulane University in 1998 and moved to the University of British Columbia in 2001, where he has been a full professor since 2006. His research has been on various aspects of geometry, topology, and algebraic geometry, often related to theoretical physics. He was awarded an Alfred P. Sloan Research Fellowship in 1999 and was elected a Fellow of the American Mathematical Society in 2017. He is currently an editor of the journal Geometry and Topology.

**Jennifer Bryan**(University of British Columbia)Jennifer Bryan is an Associate Professor at the University of British Columbia, jointly appointed in the department of Statistics and the Michael Smith Laboratories. She earned her B.A. from Yale in 1992, as a double major in Economics and German. A few years in the private sector, as an Associate in the Boston office of the Boston Consulting Group, convinced her to return to academia and she earned her Ph.D. in biostatistics from UC Berkeley in 2001. She then joined the faculty of UBC and won a Career Investigator Award from the Michael Smith Foundation for Health Research. Her main statistical interests are in applied statistics, statistical computing, and data analysis; her work is heavily motivated by problems arising in various genome-scale investigations, such as large-scale studies of genetic interaction.

**David Brydges**(University of British Columbia)David Brydges received his PhD in 1976 at the University of Michigan under the direction of Paul Federbush. He was at the University of Virginia from 1978 until 2001 when he was appointed as a Canada Research Chair at the University of British Columbia. He is known to mathematical physics and probability through his work on self-avoiding walk, Coulomb systems and the renormalisation group. Brydges received the Alfred P. Sloan Research fellowship in 1982. He has given courses in the Troisieme Cycle at Lausanne, at Centre Emile Borel, and in the NachDiplom program at ETH, Switzerland. He is serving on the Scientific Review Panel for PIMS and is the current President of the International Association of Mathematical Physics.

**Andrei Bulatov**(Simon Fraser University)Andrei Bulatov received his PhD from Ural State University in 1995. He held various faculty positions at the same university and a research position at the University of Oxford. Currently, he is now a Professor at the School of Computing Science of Simon Fraser University. His research interests include algorithms, computational complexity, constraint satisfaction problem, and applications of universal algebra. He and his students have received best paper awards at computer science conferences. He will be an ICM speaker at Seoul in 2014.

**Carlos Castillo Chavez**(Arizona State University)Carlos Castillo-Chavez (http://math.asu.edu/~chavez/) is a University Regents and a Joaquin Bustoz Jr. Professor at Arizona State University. CCC's research program is carried out at the interface of the natural and social sciences and puts emphasis on (i) the role of dynamic social landscapes on disease dispersal, dynamics and control in human and animal populations; (ii) the role of behavior (broadly understood to include addiction) on disease evolution and (iii) on the impact of local disease and behavioral dynamics across levels of organization over multiple temporal and spatial scales. CCC and collaborators have co-authored over 175 publications on HIV, influenza, Childhood diseases, STD diseases and addiction. CCC spent 18 years at Cornell University (1985-2003) and has received numerous awards including two White House Awards (1992 and 1997), the 2002 SACNAS (Society for the Advancement of Chicanos and Native Americans in Science) Distinguished Scientist Award and the Richard Tapia Award (2003). In 2003, he held the position Stanislaw M. Ulam Distinguished Scholar (http://cnls.lanl.gov/External/Ulam.php) at the Center for Nonlinear Studies at Los Alamos National Laboratory. In 2004, he was named honorary professor at Xi'an Jiaotong University in China. He has been elected fellow of the American Association for the Advancement of Science (AAAS)(http://php.aaas.org/about/aaas_fellows/list.php) and is the recipient of the AAAS Mentor award in 2007 (http://www.aaas.org/news/releases/2008/0215mentor.shtml). Carlos Castillo-Chavez is the Executive Director of two institutes: the Mathematical and Theoretical Biology Institute or MTBI (http://mtbi.asu.edu/) which focuses on providing research opportunities at the interface of the biological, computational and mathematical sciences from the undergraduate to the graduate and postdoctoral levels and SUMS (Strengthening the Understanding of Mathematics and Science) (http://mtbi.asu.edu/Institute.html). MTBI’s summer program which was established in 1996 was just recognized in 2007 (http://www.ams.org/employment/makeadiff.html) by the American Mathematical Society as a “Mathematics Program that Makes a Difference” and SUMS was recognized by a Presidential Mentorship Award in 2003. On July 1st, 2008, CCC became the founding director of the Mathematical, Computational and Modeling Sciences Center (MCMSC) and the founding director of the graduate field in applied mathematics in the life and social sciences (AMLSS) at ASU, a program that includes 20 graduate students from under- represented US minority groups.

**Alice Chang**(Princeton University)Alice Chang was born in Xi'an, China. She grew up in Taiwan and received her bachelor degree at the National Taiwan University in 1970. She moved to the United States, receiving her Ph.D. degree in mathematics at the University of California, Berkeley in 1974. Since then, she has taught at various universities in the US, including UCLA (1981-1998) and U.C. Berkeley (1989-1991). She became a Professor of Mathematics at Princeton University in 1999. She is a Sloan and Guggenheim Fellow, and was a plenary speaker at the International Congress of Mathematics in Beijing, 2002. In her thesis and the early stages of her career, her research concentrated on problems in classical harmonic analysis. In recent years, her research interests are in geometric analysis and conformal geometry. She is involved in a project applying PDE methods to classify a class of manifolds of dimension four via conformal invariants.

**Jennifer Chayes**(Microsoft Research)Jennifer Tour Chayes is an expert in the emerging field at the interface of mathematics, physics and theoretical computer science. Her current research passions include phase transitions in combinatorics and computer science, structural and dynamical properties of self-engineered networks, and auction algorithms. She is the coauthor of over 80 scientific papers and the coinventor of 11 patents. Chayes is co-founder and co-manager of the Microsoft Theory Group, as well as Research Area Manager for Mathematics and Theoretical Computer Science at Microsoft Research. She also heads the new Algorithms, Computation and E-Commerce (ACE) subgroup of the Microsoft Theory Group. In addition, she is an Affiliate Professor of Mathematics and Physics at the University of Washington, and was for many years Professor of Mathematics at UCLA. She serves on numerous institute boards, advisory committees and editorial boards, including the Board of Trustees of the Mathematical Sciences Research Institute, the Scientific Boards of the Banff International Research Station, and the Fields Institute, the Advisory Boards of the Center for Discrete Mathematics and Computer Science and the Miller Institute for Basic Research in Science, the Communications Advisory Committee of the National Academies, the Committee on Facilitating Interdisciplinary Research, the U.S. National Committee for Mathematics, the Association for Computing Machinery Advisory Committee on Women in Computing , the Leadership Advisory Council of the Anita Borg Institute, and the International Union of Pure and Applied Physics Commission on Statistical Physics. Chayes is a past Chair of the Mathematics Section of the American Association for the Advancement of Science, and a past Vice-President of the American Mathematical Society. She received her B.A. in biology and physics at Wesleyan University, where she graduated first in her class, and her Ph.D. in mathematical physics at Princeton. She did her postdoctoral work in the mathematics and physics departments at Harvard and Cornell. She is the recipient of an NSF Postdoctoral Fellowship, a Sloan Fellowship, and the UCLA Distinguished Teaching Award. She has twice been a member of the Institute for Advanced Study in Princeton. Finally, Chayes is also a Fellow of the American Association for the Advancement of Science, and a National Associate of the National Academies.

**Vladimir Chernousov**(University of Alberta)Vladimir Chernousov is the Canada Research Chair in Algebra and a Professor at the University of Alberta. He obtained his Ph.D from Minsk University in 1983. He has received prizes from Department of Mathematics of the Academy Sciences of the USSR for the proof of the Hasse principle for groups of type E_8 in 1990, Alexander von Humboldt Foundation Award in 1996 and was awarded Canada Research Chair Award in 2004. Professor Chernousov is an internationally renowned expert in the theory of linear algebraic groups. He conducts research focused on understanding the nature of algebraic groups and their classification. His research has made substantial contributions to the study of linear algebraic groups over non-closed fields. Research interests include: Linear algebraic groups, Projective homogeneous spaces and their motivic cohomology, Brauer groups, Quadratic forms, Exceptional groups and Galois cohomology. He has published 60 papers in different journals.

**Richard Cleve**(University of Waterloo)Richard Cleve’s research spans the fields of computer science and quantum physics. He specializes in computational complexity theory and cryptography. Within the last several years, a theory of quantum computing has developed that applies the notions of quantum physics to computation. The theory suggests that quantum computers – computers whose behavior is based on quantum physics – may be considerably more powerful for solving complex problems than present-day, classical computers. Cleve’s interest in quantum information processing was sparked by Peter Shor’s 1994 landmark discovery of an efficient quantum algorithm for factoring integers. Factoring large numbers is an important problem in cryptography – for example, computer security programs used in e-commerce and government computer systems are based on the fact that factoring large integers is too hard a problem for classical computers to solve. Thus, the study and further understanding of quantum computing is of vast importance to government and industry. Large-scale quantum computers have yet to be developed, however several recent experiments have successfully implemented very small prototype quantum computers. Cleve has made several contributions to quantum algorithms and quantum information theory. In particular, he played a major role in the development of quantum communication complexity, and its connection with what physicists call "non-locality." Cleve has just completed a University of Calgary Killam Resident Fellowship and is a managing editor of the journal Quantum Information and Computation. He also serves on the scientific advisory board of the Banff International Research Station.

**Ralph Cohen**(Stanford University)

**Ronald Coifman**(Yale University)Ronald Coifman is a member of the American Academy of Arts and Sciences, the Connecticut Academy of Science and Engineering, and the National Academy of Sciences. He is a recipient of the 1996 DARPA Sustained Excellence Award, the 1996 Connecticut Science Medal, the 1999 Pioneer Award of the International Society for Industrial and Applied Science, and the 1999 National Medal of Science. Coifman’s research interests include: nonlinear Fourier analysis, wavelet theory, singular integrals, numerical analysis and scattering theory, real and complex analysis; new mathematical tools for efficient computation and transcriptions of physical data, with applications to numerical analysis, feature extraction recognition and denoising. He is currently developing analysis tools for spectrometric diagnostics and hyperspectral imaging.

**Daniel Coombs**(University of British Columbia)Daniel Coombs received his BSc from the University of Sheffield in 1995 and his PhD from the University of Arizona in 2001. He subsequently held a postdoctoral position in the Theoretical Biology and Biophysics group at Los Alamos National Laboratory. He joined the faculty at the University of British Columbia in 2003. His research is primarily in the areas of theoretical immunology and within-host infectious disease dynamics. He works closely with experimental and empirical scientists in academia and industry.

**Octav Cornea**(Universite de Montreal)Octav Cornea is a Professor of Mathematics at the University of Montreal. He obtained his PhD in 1993 at the University of Rochester and, after a one year post-doctoral stay at the University of Toronto, he became a Professor at the University of Lille 1 in France. He moved to Montreal in 2003. His research is in Topology, initially in a topic of homotopy theory concerned with the Lusternik-Schnirelmann category (in particular, he co-authored a monograph on this topic which was published by the AMS in 2003) and, more recently, in symplectic topology and dynamical systems.

**Jakša Cvitanić**(California Institute of Technology)Jaksa Cvitanic obtained his Ph.D in Statistics in 1992 from Columbia University in New York. For his thesis, he was awarded the American Statistical Association Scholastic Excellence Award. He was an Assistant and Associate Professor of Statistics at Columbia University until 1999. From 1999 to 2005 he was a Professor of Mathematics and Economics at the University of Southern California, where he was also the Associate Chair. He is currently a Professor of Mathematical Finance at the California Institute of Technology. Professor Cvitanic's research interest include Financial Mathematics, Mathematical Economics, Stochastic Optimal Control and Filtering, and Backward Stochastic Differential Equations. He is a co-editor of Finance and Stochastics, and is on editorial boards of four other journals. He is a member of the Council of the Bachelier Finance Society, and is a co-author of the book "Introduction to the Economics and Mathematics of Financial Markets".

**Henri Darmon**(McGill University)Henri Darmon was cited for his remarkable work in the area of elliptic curves, particularly for his refinements of the famous Birch Swinnerton-Dyer conjecture. He has also made significant contributions to research on variants of the Fermat equation. In addition to his superb research contributions, Professor Darmon is a splendid expositor and a recent paper explaining the subtleties of Wiles' work on the Shimura-Taniyama conjecture has been widely celebrated.

**Kenneth R. Davidson**(University of Waterloo)Ken Davidson received his undergraduate degree at the University of Waterloo in 1972 and his Ph.D. from the University of California at Berkeley in 1976. He was a C.L.E. Moore instructor at M.I.T. for two years before moving to the University of Waterloo in 1978. His research interests are in operator theory and operator algebras, and he won the Israel Halperin prize in this area in 1985. He was an E.W.R.Steacie fellow 1988-90 and a Killam Research Fellow 1995-97. He was elected a fellow of the Royal Society of Canada in 1992. He has been on the editorial boards of various journals including the CMS journals and Integral Equations and Operator Theory. He has served on the CMS in various capacities including Vice President (Ontario) in 1995--97. He sat on the NSERC mathematics GSC in 1990-93, and served as chair; was a member of the NSERC Strategy Implementation Task Force in 1995, and on the Mathematics Steering Committee 1996-98. He served on the Fields Scientific Advisory Panel 1991-96, and was a co-organizer of the C*-algebra year at the institute. In addition, Ken was also the Director of the Fields Institute from 2001-2004.

**Gerda de Vries**(University of Alberta)Gerda de Vries is Professor and Associate Chair (Undergraduate) in the Department of Mathematical & Statistical Sciences at the University of Alberta. She obtained her B.Math. in Applied Mathematics and Computer Science from the University of Waterloo in 1989, and her PhD in Applied Mathematics from the University of British Columbia in 1995. She held a postdoctoral position at the Mathematical Research Branch at the National Institutes of Health in the USA (1995-1998), after which she moved to the University of Alberta. She is passionate about teaching at all levels and has won many teaching awards, including the Rutherford Award for Excellence in Undergraduate Teaching (2006) at the University of Alberta and the national-level Pacific Institute for the Mathematical Sciences Education Prize (2009). Her research interests are focussed on mathematical physiology and cell biology. Research themes include stochastic processes in biology, interfacing dynamical systems with biological data, emergent behaviour, and heterogeneous media. Her research is supported by grants from NSERC, including a Discovery Accelerator Supplement award in 2009. From 2011 to 2013, she served as elected President of the Society for Mathematical Biology.

**Charmaine Dean**(Western University)Charmaine Dean is Professor and Dean of Science at Western University. Dr. Dean’s leadership at Western’s Faculty of Science has a focus on accelerating research within the faculty, enhancing and fortifying collaborations with other faculties, with industry, government agencies and the broader community, as well as supporting a superb training environment for students. She has a strong interest in the development of innovative learning environments to support the excellent students who are drawn to Western Science. This includes pursuits as diverse as the use of technological tools for collaborative learning experiences, interdisciplinary training, individualized learning mechanisms for high achievers as well as the development of learning opportunities for the mature students. Dr. Dean has a strong interest in building a sense of connectedness in Science to work toward a collective growth and enrichment of the Faculty. Dr. Dean received her B.Sc. from the University of Saskatchewan in 1980, and her M.Math and Ph.D. degrees from the University of Waterloo in 1984 and 1988. She was 2007 President of the Statistical Society of Canada, 2002 President of the International Biometrics Society, Western North American Region, has served as President of the Biostatistics Section of the Statistical Society of Canada, and has given ten years of service to the Natural Sciences and Engineering Research Council of Canada, including two as Chair of the Statistical Sciences Grant Selection Committee and one as Chair of the Discovery Accelerator Supplement Committee for the Mathematical and Physical Sciences. She has served on the Michael Smith Foundation for Health Research Advisory Council and on selection panels for that foundation. She serves on the NIH Biostatistics Grant Review Panel; on the Board of Directors of the Pacific Institute for the Mathematical Sciences; on the Board of Directors of the Banff International Research Station; and is a member of the College of Reviewers of the UK Engineering and Physical Sciences Research Council and of the MITACS College of Reviewers. She has served on several editorial boards and is currently Associate Editor of Biometrics, of Environmetrics, of Statistics in Biosciences and Senior Editor of Spatial and Spatio-temporal Epidemiology. In 2003, Dr. Dean was awarded the CRM-SSC prize; in 2007 she was named Fellow of the American Statistical Association; and in 2007 awarded the University of Waterloo Alumni Achievement Medal; in 2010 she was named Fellow of the American Association for the Advancement of Science and in 2012 received a Trinidad and Tobago High Commission Award. Dr. Dean’s research interest lies in the development of methodology for disease mapping, longitudinal studies, the design of clinical trials, and spatio-temporal analyses. Much of this work has been motivated by direct applications to important practical problems in biostatistics and ecology. Her current main research applications are in survival after coronary artery bypass surgery, mapping disease and mortality rates, forest ecology, fire management, smoke exposure estimation from satellite imagery, and modeling of temporary and intermittent stream flow for flood analysis and predictions.

**Luc Devroye**(McGill University)Luc Devroye obtained his Ph.D. from the University of Texas in 1976, and joined the faculty of McGill University in 1977. He is the recipient of and E.W.R. Steacie Memorial Fellowship (1987), a Humboldt Research Award (2004), the Killam Prize (2005), and the Statistical Society of Canada Gold Medal (2008). His research interests include probability theory as applied to the analysis of algorithms, mathematical statistics, machine learning, pattern recognition, and random number generation.

**Darrell Duffie**(Stanford University)Duffie, a member of Stanford\'s finance faculty since 1984, is the author of books and research articles on asset valuation, credit risk, derivative securities, and over-the-counter markets. Duffie is a recent past member of the Board of The American Finance Association, a Fellow of the Econometric Society, a Research Associate of the National Bureau of Economic Research, a member of Moody\'s Academic Research Committee, and the 2003 IAFE/Sunguard Financial Engineer of the Year. He serves on the editorial boards of several economics, finance, and mathematics journals.

**Weinan E**(Princeton University)

**David Eisenbud**(Mathematical Sciences Research Institute)David Eisenbud became Director of the Mathematical Sciences Research Institute in Berkeley in the Summer of 1997, and at the same time joined the faculty of UC Berkeley as Professor of Mathematics. Before that he had been on the faculty at Brandeis University for twenty-seven years, with sabbatical time spent in Paris, Bonn, and Berkeley. In addition to his work in Berkeley, Dr. Eisenbud currently serves on several editorial boards (Annals of Mathematics, Bulletin du Soci'et'e Mathematique de France, Springer-Verlag's book series Algorithms and Computation in Mathematics). He currently serves on the Board of Mathematical Sciences and the US National Committee for Mathematics of the IMU, and he is a Vice President of the American Mathematical Society. Eisenbud's mathematical interests have ranged widely. His first paper was about permutation groups, and his thesis and subsequent few papers on non-commutative ring theory (his thesis advisors were Saunders MacLane and, unofficially, the English ring-theorist J.C. Robson.) Then he turned to commutative algebra, and subsequently to singularity theory, knot theory, and algebraic geometry. Ever since the early 70s he has used computers to produce examples in algebraic geometry and commutative algebra, and has been interested in developing algorithms to extend the power of computation in this area. In recent times he has mostly worked in commutative algebra, algebraic geometry, and computation, but his recent papers include one on a statistical application of algebraic geometry and one on juggling.

**Ivar Ekeland**(Université Paris-Dauphine)Dr. Ivar Ekeland is the Canada Research Chair in Mathematical Economics at the University of British Columbia. He is a former President of Universite Paris-Dauphine, and a former Director of the research centres CEREMADE and Institute Finance-Dauphine. He has received prizes from the French Academy of Sciences, the French Mathematical Society, and the Belgian Academy of Sciences. He is a foreign member of the Norwegian Academy of Sciences and he holds honorary doctorates from UBC and from the University of Saint-Petersburg for Economics and Finance. Dr. Ekeland is the founding editor of the "Annales de l'Institut Henri Poincare-Analyse nonlineaire" and he sits on the editorial board of many other publications. He has also written several books which are reflections on, or popularization of, mathematics. For these contributions, Dr Ekeland was awarded the "Prix Jean Rostand" by the Association des Ecrivains Scientifiques de France and the "Prix d'Alembert" by the Societe Mathematique de France. He is also a regular contributor to the journal "Nature" as well as to the magazine "Pour la Science".

**Yakov Eliashberg**(Stanford University)

**Lawrence Craig Evans**(University of California, Berkeley)Lawrence Craig Evans has been a professor at the University of California, Berkeley since 1990. He is a leading international figure in the theory of nonlinear partial differential equations, with particular emphasis nonlinear elliptic equations, Hamilton-Jacobi PDE and the calculus of variations. He has published more than 100 articles as well as 3 books, including the graduate textbook ``Partial Differential Equations'' (AMS). Professor Evans received his Ph.D. from UCLA with advisor M. G. Crandall. After faculty positions at Kentucky and Maryland, he joined the mathematics faculty at Berkeley. He has been the Director of Center for Pure and Applied Mathematics at UC Berkeley since 2004.

**Steve Evans**(University of California, Berkeley)Steve Evans received a BSc in Statistics with a University Medal from the University of Sydney in 1983 and a PhD in Mathematics from the University of Cambridge in 1987. After a stint working for the Commonwealth Bank of Australia and a post-doc at the University of Virginia, Evans joined the University of California at Berkeley in 1989, where he now has positions in Statistics and Mathematics as well as in the Graduate Group in Computational and Genomic Biology and the Graduate Group in Computational Science and Engineering. He works in the general area of stochastic processes, with a particular emphasis on probability on algebraic and topological structures, and also conducts research into applications of probability to questions in biology, particularly in the areas of population genetics, phylogenetics, metagenomics, population dynamics, transcription regulation and the modeling of aging and mortality. Evans is a recipient of the Rollo Davidson Prize, a Presidential Young Investigator Award, an Alfred P. Sloan Foundation Fellowship, and the G. de B. Robinson Prize of the Canadian Mathematical Society.

**James Feng**(University of British Columbia)James J. Feng received his B.S. (1985) and M.S. (1988) degrees from Peking University in Beijing, and his Ph.D. (1995) from the University of Minnesota, all in Fluid Mechanics. After a postdoctoral stint at the University of California, Santa Barbara, he was appointed an associate professor at the Levich Institute for Physicochemical Hydrodynamics in New York City, where he carried out research in non-Newtonian fluid dynamics and polymer rheology and taught in the Mechanical Engineering department of the City College of New York. In 2000, he received the NSF Career Award for work on multicomponent polymer flows. In 2004, he moved to the University of British Columbia (UBC) in Vancouver, Canada, as a Canada Research Chair in Complex Fluids and Interfaces, with a joint appointment in Chemical and Biological Engineering and Mathematics. He received the CFI (Canada Foundation for Innovation) Leaders Opportunity Award in 2008, and the NSERC (Natural Sci. & Eng. Res. Council) Discovery Accelerator Award in 2009. He was also a UBC Killam Faculty Research Fellow during 2010-2011, a Visiting Fellow at the Newton Institute, Cambridge University, in 2013 and 2015, and a Distinguished Scholar in Residence at the Peter Wall Institute for Advanced Studies at UBC for 2014-2015. In 2017 he received the CAIMS Research Prize of the Canadian Applied and Industrial Mathematics Society. His current research covers multiphase and interfacial fluid dynamics, cell and tissue mechanics and morphogenesis.

**Stephen E Fienberg**(Carnegie Mellon University)Stephen E. Fienberg is Maurice Falk University Professor of Statistics and Social Science at Carnegie Mellon University, and co-director of the Living Analytics Research Centre (jointly operated by Carnegie Mellon and Singapore Management University), with appointments in the Department of Statistics, the Machine Learning Department, the Heinz College, and Cylab. He joined the faculty of Carnegie Mellon in 1980. He received his B.Sc. from the University of Toronto in 1964 and his Ph.D. in Statistics from Harvard University in 1968. He has taught at the University of Chicago, the University of Minnesota, and York University, where he served as Vice President Academic. He has been Vice President of the American Statistical Association and President of the Institute of Mathematical Statistics and the International Society for Bayesian Analysis. His research includes the development of statistical methods, especially tools for the analysis of categorical data, networks, and privacy protection, from both likelihood and Bayesian perspectives. Fienberg is the author or editor of over 20 books and 500 papers and related publications. His 1975 book on categorical data analysis with Bishop and Holland, Discrete Multivariate Analysis: Theory and Practice, and his 1980 book The Analysis of Cross-Classified Categorical Data are both Citation Classics and were recently reprinted by Springer. Fienberg is Editor-in-Chief of the Annals of Applied Statistics, co-founder and Editor-in-Chief of the online Journal of Privacy and Confidentiality, and founding Editor of the Annual Review of Statistics and its Applications. He is a member of the U. S. National Academy of Sciences (NAS), and a fellow of the Royal Society of Canada, the American Academy of Arts and Sciences, and the American Academy of Political and Social Science. He is co-chair of the NAS-NRC Report Review Committee and a Member of the NAS Council.

**Daniel Freed**(University of Texas at Austin)Dan Freed is Professor of Mathematics at the University of Texas at Austin. He has also held positions at MIT and the University of Chicago as well as the Institute for Advanced Study. He works on problems in global geometry and topology, often at the interface with string theory and quantum field theory. He is the recipient of Fellowships from the Sloan and Guggenheim Foundations, as well as a Presidential Young Investigator Award from the NSF. Freed was one of the founders of the Park City/IAS Mathematics Institute. He currently serves on the Scientific Advisory Committee at MSRI.

**John Friedlander**(University of Toronto)Professor Friedlander is one of the world's foremost analytic number theorists, and is a recognized leader in the theory of prime numbers and L-functions. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Penn State in 1972. He was a lecturer at M.I.T. in 1974-76, and has been on the faculty of the University of Toronto since 1977, where he served as Chair during 1987-91. He has also spent several years at the Institute for Advanced Study where he has collaborated with E.Bombieri and many others. Friedlander is a Fellow of the Royal Society of Canada (1988), as an invited lecturer at the 1994 ICM in Zurich and delivered the CMS Jeffery-Williams Lecture in 1999. He has contributed significantly to mathematics in other ways, especially in Canada, through his role at NSERC (Mathematics GSC, 1991- 94), as Mathematics Convenor of the Royal Society of Canada (1990-93), and as a Council member (1989-95) and Scientific Advisory Panel member (1996-2000) of the Fields Institute. He has served on the Editorial Board of the Canadian Journal of Mathematics and the Canadian Mathematics Bulletin for the past 4 years.

**Jean-Marc Gambaudo**(Universite de Nice - Sophia Antipolis)Jean-Marc Gambaudo is the Director of Research at the French National Center of Scientific Research (CNRS). He received his "Doctorat d'Etat" in 1987 from the University of Nice-Sophia Antipolis (UNSA). He started his career at UNSA, and then he moved to the "Ecole Normale Supï¿½rieure" of Lyon. Afterwards, he joined the University of Burgundy and became the head of the "Institut de Mathï¿½matiques de Bourgogne". He returned to Nice in 2006. He has been visiting for long periods in many institutes in the United States, Brazil and Chile. Since September 2006 and besides his research activities, Jean-Marc Gambaudo has been elected deputy director for mathematics at CNRS. Gambaudoï¿½s research interests concern geometric theory of dynamical systems, geometry and topology in low dimension, topological methods in hydrodynamics, aperiodic tilings and quasicrystals, statistical mechanics, and applications.

**Peter Glynn**(Stanford University)Peter W. Glynn is the current Chair of the Department of Management Science and Engineering at Stanford University. He received his Ph.D in Operations Research from Stanford University in 1982. He then joined the faculty of the University of Wisconsin at Madison, where he held a joint appointment between the Industrial Engineering Department and Mathematics Research Center, and courtesy appointments in Computer Science and Mathematics. In 1987, he returned to Stanford, where he joined the Department of Operations Research. He is now the Thomas Ford Professor of Engineering in the Department of Management Science and Engineering, and also holds a courtesy appointment in the Department of Electrical Engineering. From 1999 to 2005, he served as Deputy Chair of the Department of Management Science and Engineering, and was Director of Stanford's Institute for Computational and Mathematical Engineering from 2006 until 2010. He is a Fellow of INFORMS and a Fellow of the Institute of Mathematical Statistics, has been co-winner of Best Publication Awards from the INFORMS Simulation Society in 1993 and 2008, was a co-winner of the Best (Biannual) Publication Award from the INFORMS Applied Probability Society in 2009, and was the co-winner of the John von Neumann Theory Prize from INFORMS in 2010. His research interests lie in simulation, computational probability, queueing theory, statistical inference for stochastic processes, and stochastic modeling.

**Randy Goebel**(University of Alberta)R.G. (Randy) Goebel is Professor of Computing Science at the University of Alberta, in Edmonton, Alberta, Canada, and a principle investigator in the Alberta Innovates Centre for Machine Learning. He is also Chief Scientist of Alberta Innovates Techology Futures, a publicly-funded Alberta research organization that attempts to bridge the innovation gap between basic and applied research. He holds B.Sc., M.Sc. and Ph.D. degrees in computer science from the University of Regina, Alberta, and British Columbia, and has had faculty appointments at the Unviersity of Waterloo, University of Tokyo, Multimedia University (Malaysia), Hokkaido University, and has worked at a variety of research institutes around the world, including DFKI (Germany), NICTA (Australia), and NII (Tokyo). His current research interests include applications of machine learning to systems biology, visualization, and web mining, as well as work on natural language processing, web semantics, and belief revision. He has experience working on industrial research projects in crew scheduling, pipeline scheduling, and steel mill scheduling, as well as scheduling and optimization projects for the energy industry in Alberta.

**Xavier Gomez-Mont**(CIMAT)

**Eyal Goren**(McGill University)Eyal Goren received his Ph.D. from the Hebrew University in Jerusalem (1997). After postdoctoral studies at Harvard and Utrecht universities, he was a CICMA postdoctoral fellow at Montreal and joined McGill as faculty in 1999, where he is now an associate professor. He received a 5-year "Strategic Professor" award from Quebec, and held visiting positions at the Max-Planck Institute, Padova university, the Hebrew University (Lady Davis Fellow) and Microsoft Research. Goren's research is in arithmetic geometry; more specifically, mod p and p-adic geometry of moduli spaces of abelian varieties, modular forms and class field theory, expander graphs and their applications.

**Timothy Gowers**(Cambridge University)William Timothy Gowers is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at Cambridge University, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College. In 1998 he received the Fields Medal for his research connecting the fields of functional analysis and combinatorics.

**Vivek Goyal**(3dim)Vivek K Goyal received the B.S. degree in mathematics and the B.S.E. degree in electrical engineering from the University of Iowa, where he received the John Briggs Memorial Award for the top undergraduate across all colleges. He received the M.S. and Ph.D. degrees in electrical engineering from the University of California, Berkeley, where he received the Eliahu Jury Award for outstanding achievement in systems, communications, control, or signal processing. He is currently Associate Professor of Electrical Engineering at the Massachusetts Institute of Technology. His research interests include source coding theory, sampling, quantization, magnetic resonance imaging, and optical imaging. He was awarded the 2002 IEEE Signal Processing Society Magazine Award and an NSF CAREER Award, and his students have been awarded several thesis and conference best paper awards. He served a six-year term on the IEEE Signal Processing Society's Image and Multiple Dimensional Signal Processing Technical Committee and was a plenary speaker at IEEE Data Compression Conference and IEEE Multimedia Signal Processing Workshop. He will give a tutorial on teaching signal processing at IEEE ICASSP 2012. He is a Technical Program Committee Co-chair of IEEE ICIP 2016 and a permanent Conference Co-chair of the SPIE Wavelets and Sparsity conference series.

**Andrew Granville**(Université de Montréal)Andrew Granville is the Canadian Research Chair in Number Theory at the Université de Montréal, and an associate director of Centre de Recherche mathématiques. Dr Granville's primary research interest is in analytic number theory, although he has recently been interested in the exciting new field of additive combinatorics. He also dabbles in algebraic number theory, arithmetic geometry, combinatorics, harmonic and functional analysis, and theoretical computer science.He is the author of over 100 research articles, more than 20 expository articles, several books, a play and is currently working on a (mathematical) graphic novel. He works with a research team of about a dozen students and postdocs, and has helped develop the Montréal number theory seminar into one of the liveliest anywhere. Dr Granville has received several awards for research including the Jeffery-Williams prize, for expository writing including the Chauvenet prize, and for academic leadership including the (U.S.) Presidential Faculty Fellowship. Various honors include speaking at the 1994 International Congress of Mathematicians, and giving named lectureships in five different countries. Dr Granville has served on advisory boards for the CRM as well as for MSRI, the Fields' Institute, and the Cryptography Research Institute. He has been on the editorial boards of more than a dozen journals and several book series, and served on various external review panels.

**Robert Gray**(Stanford University)Robert M. Gray received the B.S. and M.S. degrees from M.I.T. in 1966 and the Ph.D. degree from U.S.C. in 1969, all in Electrical Engineering. Since 1969 he has been with Stanford University, where he is currently the Lucent Technologies Professor of Engineering. His research interests are in information theory and signal processing, especially in the theory and practice of quantization, compression, and classification. He served as Editor-in-Chief of the IEEE Transactions on Information Theory (1980-83) and is the EIC of Foundations and Trends in Signal Processing. He is a Fellow of the Institute of Mathematical Statistics and the IEEE and was a John Simon Guggenheim Foundation Fellow at the University of Paris XI (1982). He received Centennial (1984) and Third Millenium (2000) medals from the IEEE; the 1993 Society Award, the 1998 Technical Achievement Award, and the 2005 Meritorious Service Award from the IEEE Signal Processing Society; and a Golden Jubilee Award for Technological Innovation (1998) and the 2008 Claude E. Shannon Award from the IEEE Information Theory Society. He received a 2002 Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM) and was elected to the US National Academy of Sciences in 2007.

**Mark Green**(University of California, Los Angeles)Mark Green obtained his PhD from Princeton, where his thesis adviser was Phillip Griffiths. After teaching at Berkeley and MIT, he moved to UCLA as an Assistant Professor in 1975. Dr. Green's research has taken him into several areas of mathematics - several complex variables, differential geometry, commutative algebra, Hodge theory and algebraic geometry. He received an Alfred P. Sloan fellowship and was an invited speaker at the International Congress of Mathematicians in Berlin. Along with Eitan Tadmor, he was one of IPAM's Founding Co-Directors. He has been Director of IPAM since 2001.

**David Gross**(University of California, Santa Barbara)David Gross joined the Institute for Theoretical Physics at the University of California, Santa Barbara in January 1997. He received his Ph.D. from the University of California, Berkeley in 1966 and then was a Junior Fellow at Harvard. In 1969 he went to Princeton where he was appointed Professor of Physics in 1972, and later Eugene Higgins Professor of Physics, and Thomas Jones Professor of Mathematical Physics. Dr. Gross was an Alfred P. Sloan Foundation Fellow (1970-74), was elected Fellow of the American Physical Society in 1974, Fellow of the American Academy of Arts and Sciences in 1985, Member of the National Academy of Sciences in 1986 and Fellow of the American Association for the Advancement of Science in 1987. He is the recipient of the J. J. Sakurai Prize of the American Physical Society in 1986, a MacArthur Foundation Fellowhip Prize in 1987, the Dirac Medal in 1988, the Oscar Klein Medal in 2000 and the Harvey Prize of the Technion in 2000. He also has received two honorary degrees. In 2004 David Gross was selected to receive France's highest scientific honor, the Grande Médaille D'Or, for his contributions to the understanding of fundamental physical reality. The Frederick W. Gluck Chair in Theoretical Physics, an endowed chair for the director of the Kavli Institute for Theoretical Physics, was established in 2002 with a generous gift from UCSB trustee Fred Gluck.

**Arvind Gupta**(University of British Columbia)Arvind Gupta became the Program Leader of the MITACS NCE at the end of 1999. Dr. Gupta received his Ph.D. from the University of Toronto in 1991 under the supervision of Dr. Steve Cook. After spending one year as an NSERC PDF at the University of Waterloo, he joined the faculty of Simon Fraser University in September, 1991. His main research interests are in the areas of combinatorics, optimization and complexity theory. Dr. Gupta was one of the founders of PIMS and he served as SFU Site Director and Deputy Director from 1996 until May 1999. He was instrumental in establishing the highly successful PIMS industrial outreach strategy. He was a founder of both the PIMS Industrial Problem Solving Workshop and the PIMS Summer Industrial Graduate Training Camp.

**Robert Guralnick**(University of Southern California)Robert Guralnick received his Ph. D. from UCLA in 1977 and is currently a Professor of Mathematics at the University of Southern California. His research interests include linear and permutation representations of finite and algebraic groups with applications to number theory and algebraic geometry. He was an ICM speaker at Seoul in 2014, a PIMS distinguished lecturer and a plenary speaker at the British Colloquium. He gave a plenary talk at the annual AMS meeting in 2013. He was the G. C. Steward fellow at Gonville and Caius in Cambridge in 2009 and has held visiting appointments at Yale, Caltech, Princeton, Cambridge, IAS, the Newton Institute and MSRI. He was an inaugural Simons Foundation Fellow in 2013 (spending the year at Princeton and IAS). He won the Frank Nelson Cole Prize in Algebra in 2018 and will be a plenary speaker at the joint AMS-VMS in 2019.

**Peter Guttorp**(Norwegian Computing Center)Peter Guttorp, Professor and Chair of Statistics, Director of the National Research Center for Statistics and the Environment, and member of the QERM interdisciplinary faculty, obtained a degree in journalism from the Stockholm School of Journalism in 1969. He received a B.S. in mathematics, mathematical statistics, and musicology from the University of Lund, Sweden, in 1974, and a Ph.D. in Statistics from the University of California at Berkeley, in 1980. He joined the University of Washington faculty in September 1980. Dr. Guttorp's research interests include uses of stochastic models in scientific applications in hydrology, atmospheric science, geophysics, environmental science, and hematology. He is an associate editor of International Statistical Review, and a member of the Editorial Boards of Environmental and Ecological Statistics and Environmetrics. He is also past President of the International Environmetrics Society, and a member of the ISI Committee on Environmental Statistics. He is a fellow of the American Statistical Association and an elected member of the International Statistical Institute. During 2004-2005 he was the Environmental Research Professor of the Swedish Institute of Graduate Engineers.

**Pavol Hell**(Simon Fraser University)Pavol Hell received his undergraduate education at Charles University in Prague, and his doctorate (in 1973) at the Universite de Montreal. After postdoctoral years in British Columbia, he held his first tenured position at Rutgers University in New Jersey. He moved back to British Columbia in 1980, to join the Computing Science Department (now School) at Simon Fraser University, where he holds a position of Full Professor. He has held a number of visiting positions, most recently at the Universite de Nice - Sophia Antipolis, the Federal University of Rio de Janeiro, and Charles University. He was elected Chair of the Executive Board of the SIAM Activity Group in Discrete Mathematics, 2006 - 2008, and during his term helped to establish the SIAM Denes Konig Prize in Discrete Mathematics. He has served on the NSERC Grant Selection Committee 331, Computing and Information Sciences – B, 2005 - 2008. He is the Managing Editor of the Journal of Graph Theory, as well a member of several other editorial boards. His research interests include graph algorithms, optimization, constraint satisfaction, and complexity, with emphasis on homomorphisms of graphs and digraphs.

**Sheila Hemami**(Cornell University)Sheila S. Hemami received her B.S.E.E. degree from the University of Michigan in 1990, and M.S.E.E. and Ph.D. degrees from Stanford University in 1992 and 1994, respectively. Her Ph.D. thesis was entitled "Reconstruction of Compressed Images and Video for Lossy Packet Networks" and she was one of the first researchers to work on what we now call "error concealment." She was with Hewlett-Packard Laboratories in Palo Alto, California in 1994 and worked on video-on-demand. She joined the School of Electrical Engineering at Cornell University in 1995, where she holds the title of Professor and directs the Visual Communications Laboratory. Dr. Hemami's research interests broadly concern communication of visual information, both from a signal processing perspective (signal representation, source coding, and related issues) and from a psychophysical perspective. Dr. Hemami is an IEEE Fellow and has held various visiting positions, most recently at the University of Nantes, France and at Ecole Polytechnique Federale de Lausanne, Switzerland. She has received numerous college and national teaching awards. She is an active volunteer in the IEEE Signal Processing Society.

**Helmut Hofer**(Institute for Advanced Studies)Helmut Hofer received his Ph.D. in 1981 from the University of Zurich, Switzerland. He works in the fields of symplectic geometry, dynamical systems and partial differential equations. He is best known for the discovery of a remarkable geometry of symplectic diffeomorphism groups, meanwhile called Hofer's Geometry. In 1998 he was a plenary lecturer at the International Congress in Berlin, and an invited speaker at the International Congress in Kyoto in 1990. He was the recipient of a Sloan Fellowship and shared the 1999 Ostrowski Prize with A. Beilinson. Dr. Hofer also serves as the chairman of the scientific advisory board of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. He is editor of various mathematical journals.

**G. M. (Bud) Homsy**(University of California Santa Barbara)G. M. "Bud" Homsy obtained all his degrees in Chemical Engineering (BS: UC Berkeley, MS/PhD: U. Illinois). After a NATO Postdoctoral Fellowship at Imperial College, London, Professor Homsy joined the Chemical Engineering faculty at Stanford University in 1970, where he taught for 30 years before joining the faculty of Mechanical Engineering at UC Santa Barbara in 2001. He will join the Mathematics Department at the University of British Columbia in early 2010. Professor Homsy’s field of research is fluid mechanics and hydrodynamic stability and he has published over 150 papers in the lead journals in the field. He has made contributions in the areas of stability of time dependent flows; flow through porous media, including pore level modeling and viscous fingering; thermal convection; fluid-particle systems, including fluidized beds and suspensions; interfacial flows, including Marangoni flows, coating flows, electrohydrodynamics, and contact line dynamics; and non-Newtonian flows. Professor Homsy has held many professional positions, including Vice-Chair and Chair of the APS Division of Fluid Dynamics, two terms as Department Chair at Stanford, Chairman of the Board of USRA, Department Chair at UCSB, and Associate Editorships of SIAM J. Applied Math, Int. J. Multiphase Flow, and Physics of Fluids. He is a Fellow of the APS and was awarded a Bing Fellowship at Stanford University for service to undergraduate education. His major invited speaker positions include the Midwest Mechanics speaker, the Talbot Lecturer at UIUC, the Batchelor Visitor at DAMTP, Cambridge and distinguished lectureships at the University of New Mexico, the University of Tennessee, and the University of British Columbia. He has held many visiting professorships in the US and Europe, including ESPCI, Paris; University of Paris VI; University of Marseille; University of Toulouse, and was a PIMS Visitor at U. of British Columbia. He was the Principal Investigator for the production of "Multimedia Fluid Mechanics," Cambridge (2001), and its second edition (2008). He is the recipient of the APS Fluid Dynamics Prize for 2004 and was elected to the US National Academy of Engineering in 2006.

**Gerhard Huisken**(Universitaet Tuebingen)Gerhard Huisken is the director of the section "Geometric Analysis and Gravitation" at the Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute) in Potsdam, Germany, since 2002. He holds honorary professorships in Mathematics at Free University Berlin and at Tubingen University. He obtained his PhD from Heidelberg University in 1983 and spend a total of eight years at the Australian National University until he was appointed professor at Tubingen University in 1992. He held visiting professorships at UC San Diego, Stanford University and Princeton University and received a Leibniz prize of the German research foundation in 2003. He is an editor of "Crelle Journal" and "Calculus of Variations". Huisken's research interests are nonlinear partial differential equations, differential geometry and applications to general relativity. Specific interests concern geometric evolution equations such a mean curvature flow with their regular and singular behaviour and their monotonicity properties.

**Craig Huneke**(University of Virginia)Craig L. Huneke is a professor of mathematics at the University of Kansas. He received his PhD from Yale University in 1978. He is recipient of many prestigous awards and appointments including; Contemporary Mathematics Editorial Committee,1991–1995 (Managing Editor 1993–1995); Bull. Amer. Math. Soc.Editorial Committee, 1999–2002; Committee on Meetings and Conferences,2002–2005; Committee to Select Steele Prize, 2003–2006; Committee to Select the Winner of the Cole Prize (in Algebra) for 2006, 2005–2006. Michigan Jr. Fellow, 1978–1981; NSF Postdoctoral Fellowship, 1981–1982; Sloan Postdoctoral Fellowship, 1984; Fulbright Scholar, 1998; Scientific Advisory Committee, Banff International Research Station, 2001–2003. Other Editorial Boards: Math. Research Letters, 1993–, J. Algebra, 1996–2005, Collect. Math., 2000–,Ann. Fac. Sci. Toulouse Math., 2003–.

**Jacques Hurtubise**(McGill University)Jacques Hurtubise (BSc, Université de Montréal; PhD, Oxford University) is a professor in the Department of Mathematics and Statistics. He came to McGill in 1988 as an associate professor and was promoted to full professor in 1994. He has served on numerous academic, selection and administrative committees at McGill and externally, at the local, provincial, national and international levels. From 1999 to 2003, he was director of the Centre de recherches mathématiques at the Université de Montréal. He also served as president of the Réseau de calcul et de modélisation mathématique at the Université de Montréal during the same period. He has just been elected to the Royal Society of Canada, Academy of Science.

**Lisa Jeffrey**(University of Toronto)Lisa Jeffrey is a Professor in Mathematics at the University of Toronto at Scarborough. She did her undergraduate degree in physics at Princeton University and then went to to obtain an M.A. in mathematics from Cambridge University and a D. Phil. in mathematics from Oxford University. She has twice held the position of Member at the Institute for Advanced Study at Princeton and held faculty positions at Princeton and McGill before coming to University of Toronto in 1998. Her research is on the border between mathematics and theoretical physics. She uses techniques from pure mathematics to prove results obtained by theoretical physics. Professor Jeffrey's field of research (symplectic geometry) is the natural mathematical framework for classical mechanics. She is an editor of Transactions of the American Mathematical Society and was a member of the Scientific Advisory Panel of the Fields Institute from 2000 to 2004. She was awarded the E.W.R. Steacie Fellowship in 2004.

**Bill Johnson**(Texas A&M University)Bill Johnson received his Ph.D. from Iowa State University in 1969. He is now Distinguished Professor of Mathematics, A.G. & M.E. Owen Chair of Mathematics, and Director of the Workshop in Analysis and Probability at Texas A&M University. He previously held regular appointments at the University of Houston (Assistant Professor, 1969-71) and Ohio State University (Assistant Professor, 1971-73; Associate Professor 1973-74; Professor, 1974-84). Johnson has given invited hour addresses to the American Mathematical Society and the Canadian Mathematical Society. He is the 2007 recipient of the Stefan Banach Medal, awarded by the Presidium of the Polish Academy of Sciences for "for outstanding achievements in mathematical sciences". He has served on the editorial boards of the Transactions of the American Mathematical Society, the Illinois Journal of Mathematics, Geometric and Functional Analysis, Mathematische Annalen, Positivity, the Houston Journal of Mathematics, and Extracta Mathematicae. From his base in geometrical functional analysis, Johnson has done research in probability, operator theory, complex analysis, approximation theory, and metric geometry. He is both amused and chagrined that his most frequently cited result is a lemma (Googling "Johnson-Lindenstrauss lemma", with quotes, yields 45,000 hits).

**Valentine Kabanets**(Simon Fraser University)Valentine Kabanets received a PhD from the University of Toronto in 2001 under the supervision of Steve Cook. After spending one year as a member of the Institute for Advanced Study, Princeton, and two years as a postdoctoral fellow at the University of California, San Diego, he joined the School of Computing Science at Simon Fraser University, where he is currently an associate professor. His research interests are in computational complexity. He is a recipient of several best paper awards at top theoretical computer science conferences.

**Niky Kamran**(McGill University)Niky Kamran was born in Belgium in 1959. He is a James McGill professor in the Department of Mathematics and Statistics at McGill University. He has been a member of the Institute for Advanced Study and the Institut des Hautes Etudes Scientifiques. He works in differential geometry and mathematical physics. His research interests include the study of wave equations in black hole geometries and the theory of quasi-exactly solvable systems. Niky has served as Editor-in-Chief of the Canadian Journal of Mathematics, and as Chair of the NSERC Grants Selection Committee 337. He was elected a Fellow of the Royal Society of Canada in 2002 and he is currently a Killam Fellow of the Canada Council for the Arts.

**Yael Karshon**(University of Toronto)Yael Karshon is a Professor of Mathematics at the University of Toronto. She received her B.Sc. and M.Sc. from Tel-Aviv Univerity, and in 1993 she completed her Ph.D. at Harvard University. After holding a C.L.E. Moore Instructorship at M.I.T., she joined the Hebrew University of Jerusalem. In 2002 she moved to Toronto with her family. She received the Yig'al Alon fellowship (1997-2000), the University of Toronto McLean award (2005), and the Canadian Mathematical Society Krieger-Nelson prize (2009). Her main research contributions are in symplectic geometry with emphasis on equivariant techniques. She enjoys working with Ph.D. students and postdoctoral fellows.

**Svetlana Katok**(The Pennsylvania State University)Svetlana Katok grew up in Moscow, and earned a masters degree from Moscow State University in 1969. She emigrated to the USA in 1978 and earned her Ph.D. from the University of Maryland, College Park in 1983 under the supervision of Don Zagier. She was awarded an NSF postdoctoral fellowship and was associated with Caltech and four campuses of the University of California before moving to Penn State in 1990, where she was promoted to full professor in 1993. Her mathematical interests center on the interaction between number theory, geometry and dynamical systems with the latter field, her first mathematical specialty, coming to the fore in the last decade. She serves as managing editor of Journal of Modern Dynamics and Electronic Research Announcements in Mathematical Sciences. She has served on many AMS, NSF and NRC committees and panels and was a Member-at-Large of the AMS Council for 1993-1996. In 2001 she received the Eberly College of Science Alumni Society Distinguished Service Award at Penn State. She was the 2004 Emmy Noether Lecturer of the Association for Women in Mathematics. In 2012 she became a fellow of the American Mathematical Society.

**Carlos Kenig**(University of Chicago)Carlos E. Kenig was born in Buenos Aires, Argentina on November 25, 1953. He obtained his Phd at the University of Chicago in 1978, under the direction of A.P.Calderon. After being on the faculty at Princeton University and the University of Minnesota, he returned to the University of Chicago in 1985, as Professor of Mathematics. He currently is the Louis Block Distinguished Service Professor at the University of Chicago. Kenig has been a Sloan Fellow, a Guggenheim Fellow and in 1984 was awarded the Salem Prize. Kenig was elected as a Fellow of the American Academy of Arts and Sciences in 2002.

**Nancy Kopell**(Boston University)Nancy Jane Kopell was born in New York City on November 8, 1942. She received her B.S. in mathematics from Cornell University and her Ph.D. in 1967 from the University of California, Berkeley, with a dissertation on "Commuting diffeomorphisms" under the direction of Stephen Smale. Kopell held a C.L.E. Moore Instructorship at the Massachusetts Institute of Technology from 1967 to 1969, then joined the faculty at Northeastern University. In 1978 she was promoted to full professor at Northeastern. Since 1986 she has been a professor of mathematics at Boston University. In July 1990, Nancy Kopell was awarded a MacArthur Foundation Fellowship for a five-year period. Kopell is currently co-director of the Center for BioDynamics (CBD) at Boston University. This multidisciplinary, interdepartmental center aims to train undergraduates, graduates, and postdoctoral fellows in leading techniques from dynamical systems theory and its applications to biology and engineering. She lists her current research interests as mathematical modeling of networks of neurons in vertebrates and invertebrates; special interest in networks having oscillatory behavior, such as those governing rhythmic motor behavior, thalamocortical and hippocampal networks; and use of mathematics to investigate how properties of cells and small networks affect the dynamics of the larger networks that contain them. Kopell was elected to the National Academy of Sciences in 1996. In April 2000, she was named Boston University's first William Goodwin Aurelio Professor of Mathematics and Science.

**Thomas Kurtz**(University of Wisconsin)Thomas G. Kurtz received his PhD in Mathematics from Stanford University in 1967. He has been on the faculty at the University of Wisconsin - Madison since that time, and is currently Paul Levy Professor in the Departments of Mathematics and Statistics. He served as Mathematics Department chair from 1985-1988 and as Director of the Center for the Mathematical Sciences from 1990-1996. He is a Fellow of the Institute of Mathematical Statistics and is currently IMS President. He was recently elected as a Fellow of the American Academy of Arts and Sciences. His research interests include limit theorems for stochastic differential equations, particle representations of measure-valued processes, stochastic partial differential equations, filtering for Markov processes, large deviations, and modeling of spatial point processes. Application areas include communication networks, genetics, and finance.

**Rachel Kuske**(University of British Columbia)Rachel Kuske holds a Canadian Research Chair in Applied Mathematics at UBC. Following her Ph.D. received in 1992 from Engineering Sciences and Applied Math at Northwestern University, she was an NSF and NSF-NATO Postdoctoral Fellows and a Szego Assistant Professorship at Stanford University. She heldÂ faculty positions at Tufts University and the University of Minnesota, where she was aÂ McKnight Landgrant Professor and Associate Director of the Minnesota Center for Industrial Mathematics. Kuske's mathematical interests vary widely over a number of areas of applied mathematics, including modelling in stochastic dynamics, structural dynamics, mathematical finance, and mathematical biology. Recent invited lectures include a Topical Lecture at the SIAM Annual Meeting and an invited mini-symposium on Noise in Complex Systems at the AAAS Annual Meeting. She is on the editorial board for SIAM Journal of Applied Math. In addition to being co-organizer and academic expert at a number of Industrial Problems Workshops at the IMA and PIMS. Kuske was co-chair for the SIAM Applied Dynamical Systems in 2005. She is the founder and director for the AWM Mentor Network and is coordinating projects supporting Women in Science at various levels.

**Matilde Lalin**(Université de Montrèal)Matilde Lalin is an associate professor at the Université de Montréal. She received her PhD in 2005 from the University of Texas at Austin where she was a Harrington Fellow. She was a member at the Institute for Advanced Study, a Clay Liftoff Fellow, a PIMS postdoctoral fellow at the University of British Columbia, and an Assistant Professor at the University of Alberta before moving to her present institution. In addition, she held visiting positions at the Mathematical Sciences Research Institute, the Institut des hautes études scientifiques, and the Max Planck Institute for Mathematics. Her research interests lie in Number Theory and related areas and they include Mahler measure, special values of L-functions, and arithmetic statistics. She has written more than 25 articles in these topics.

**Kristin Lauter**(Microsoft Research)Kristin Lauter is a Principal Researcher, Research Manager of the Cryptography Research Group at Microsoft Research in Redmond, Washington, and an Affiliate Professor at the University of Washington. Her research focuses on number theory and algebraic geometry, with applications to cryptography and coding theory. Lauter received her BA, MS, and PhD degrees in mathematics from the University of Chicago, in 1990, 1991, and 1996, respectively. Prior to joining Microsoft Research, she held positions as T.H. Hildebrandt Research Assistant Professor at the University of Michigan (1996-1999), a Visiting Scholar at Max-Planck-Institut für Mathematik in Bonn, Germany (1997), and a Visiting Researcher at the Institut de Mathématiques Luminy in France (1999). From 2010-2013 she was a member of the Senior Leadership Team for the Microsoft Research XCG Lab. Lauter has published extensively in mathematics and computer science, with over 50 published research articles and 3 edited volumes. In 2008, Lauter, together with her coauthors, was awarded the Selfridge Prize in Computational Number Theory. Her research has been covered in scientific publications such as Science, American Scientist, and Technology Review. Lauter has given an Invited Address at the SIAM Annual Meeting and Invited Addresses at regional meetings of the AMS and MAA. She has served on the Executive Committee of the Association for Women in Mathematics and on the editorial boards for Journal of Algebra and Its Applications and International Journal of Information and Coding Theory. She has served as Program Chair and on the Program Committee for many cryptography conferences in computer science, and she serves on the Advisory Board for SHARPS, the Strategic Healthcare IT Advanced Research Projects on Security.

**Robert Lazarsfeld**(Stony Brook University)Robert Lazarsfeld is a Professor of Mathematics at the University of Michigan. He was an undergraduate at Harvard, and received his PhD from Brown University in 1980. He served on the faculty of UCLA until 1997, at which time he moved to Michigan. Lazarsfeld works in complex algebraic geometry. In recent years, his research has centered around higher-dimensional geometry, and applications of the techniques developed in that field to questions in algebra. He recently completed a two-volume monograph on positivity in algebraic geometry. He is an editor of the Journal of the AMS, and in 2005 was the AMS Colloquium Lecturer.

**Randy LeVeque**(University of Washington)Randy LeVeque received his Ph.D. in Computer Science from Stanford University in 1982. He has been in the Applied Mathematics Department at UW since 1985 and has also held positions at the Courant Institute (NYU), UCLA, and ETH-Zurich. He is a Fellow of SIAM of the AMS, and is currently Chair of the SIAM Journals Committee. He received a Presidential Young Investigator Award in 1987 and was an invited speaker at ICM 2006 in Madrid. LeVeque's main research interests are in the development, analysis, and application of numerical methods for partial differential equations. He is the primary developer of the Clawpack software package and the author of three books on numerical methods for differential equations.

**Mark Lewis**(University of Alberta)Dr. Mark Lewis is a faculty member at the University of Alberta where he is the Senior Canada Research Chair in Mathematical Biology and directs the Centre for Mathematical Biology. He obtained his doctorate from the University of Oxford in 1990 in mathematical biology. He was a faculty member at the University of Utah until 2001, and has also held visiting and research fellowships at Princeton University and Imperial College, University of London. He is Past President of the Society for Mathematical Biology, and is on the editorial boards for a number of journals including Journal of Mathematical Biology, IMA Journal of Mathematic Medicine and Biology, Ecology and Ecological Monographs. Lewis has served on a number of advisory boards, including and the Journal of Theoretical Biology Advisory Board and Scientific Advisory Board for the Banff International Research Station for Mathematical Innovation and Discovery. His research has been recognized by a Sloan Research Fellowship and a National Young Investigator Award (US NSF. Lewis’ research is in mathematical biology and ecology, including modeling and analysis of nonlinear PDE and integral models in population dynamics and ecology. Applications, made to case studies with detailed data and biology, include: wolf territories, elk migration in Yellowstone Park, spatial spread and impact of introduced pest species, vegetation shift in response to climate change and recolonization of Mt. St. Helens. He has also been a member of the PIMS Board of Directors since 2004.

**Elon Lindenstrauss**(Hebrew University)Elon Lindenstrauss is a Professor at the Einstein Institute of Mathematics of the Hebrew University of Jerusalem. Before going back to Jerusalem he had a Professor position at Princeton University. Lindenstrauss' main topic of research is homogeneous dynamics and its interconnections with number theory as well as spectral theory. For his work he has received several prizes, in particular the Fields Medal in 2010. His research interests are Ergodic theory, dynamical systems and number theory.

**Laszlo Lovasz**(Eötvös Loránd University)

**Michael C. Mackey**(McGill University)Michael C. Mackey received his undergraduate degree in Mathematics from the University of Kansas in 1963, and his doctorate in Physiology and Biophysics from the University of Washington in 1968. Following military service he joined the McGill University faculty in 1971 as a member of the Department of Physiology. He is currently the Joseph Morley Drake Professor of Physiology at McGill and holds associate membership in the McGill Departments of Mathematics and Physics, teaching in all three departments. He is also the Director of the Centre for Nonlinear Dynamics in Physiology and Medicine. Prof. Mackey received a research prize in 1993 from the Alexander von Humboldt Stiftung, was elected to the Royal Society of Canada in 1999, was a Fellow of the Hanse Wissenschaftkolleg in 2000, and was the Leverhulme Visiting Professor of Mathematical Biology at Oxford University in the 2001 and 2002 academic years. His research interests include the dynamics of physiological systems, and the foundations of statistical mechanics and quantum mechanics. Links to Learn More: http://www.cnd.mcgill.ca/bios/mackey/mackey.html

**Jitendra Malik**(University of California, Berkeley)Jitendra Malik was born in Mathura, India in 1960. He received the B.Tech degree in Electrical Engineering from Indian Institute of Technology, Kanpur in 1980 and the PhD degree in Computer Science from Stanford University in 1985. In January 1986, he joined the university of California at Berkeley, where he is currently the Arthur J. Chick Professor and Chair of the Department of Electrical Engineering and Computer Science. He is also on the faculty of the Cognitive Science and Vision Science groups. His research interests are in computer vision and computational modeling of human vision. His work spans a range of topics in vision including image segmentation and grouping, texture, stereopsis, object recognition, image based modeling and rendering, content based image querying, and intelligent vehicle highway systems. He has authored or co-authored more than a hundred research papers on these topics. He received the gold medal for the best graduating student in Electrical Engineering from IIT Kanpur in 1980, a Presidential Young Investigator Award in 1989, and the Rosenbaum fellowship for the Computer Vision Programme at the Newton Institute of Mathematical Sciences, University of Cambridge in 1993. He received the Diane S. McEntyre Award for Excellence in Teaching from the Computer Science Division, University of California at Berkeley, in 2000. He was awarded a Miller Research Professorship in 2001. He serves on the Editorial Board of the International Journal of Computer Vision.

**Rafe Mazzeo**(Stanford University)Rafe Mazzeo was an undergraduate at MIT and earned his PhD from there as well in 1986. He moved directly to Stanford University, where he has been ever since, except for a two year period in the early 1990's at the University of Washington, and is currently Department Chair. He has been an NSF Postdoctoral Fellow, a Sloan Foundation Fellow and recipient of an NSF Young Investigator Award. He delivered the Nachdiplom Lectures at ETH in Zurich in 2004. He is currently Managing Editor of Communications in Partial Differential Equations, and is on the editorial board of the AMS series, Graduate Studies in Mathematics and is just beginning a term on the editorial board of the Notices of the American Math Society. Mazzeo is also deeply interested in educational opportunities for gifted youth, and was a founder of SUMaC, the Stanford University Math Camp, and has directed and taught in that program for over fifteen years. He also serves on the advisory board of Stanford's Educational Program for Gifted Youth. Mazzeo's research interests encompass a variety of topics in linear and nonlinear geometric analysis, including spectral geometry, index theory, scattering theory, Einstein metrics and other special geometries, minimal and constant mean curvature surfaces, etc.

**Peter McCullagh**(University of Chicago)Peter grew up in Northern Ireland. Before moving to Chicago, he obtained his Bachelor's degree in mathematics from the University of Birmingham, and his doctoral degree in statistics from Imperial College. He has held visiting positions at the University of British Columbia and at Bell Labs. He is a Fellow of the Institute of Mathematical Statistics, the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the Royal Society. Peter's research focuses on probabilistic modelling, statistical theory, and the application of statistical methods in diverse areas, particularly in scientific research such as biostatistics, agricultural research, ecology and animal behaviour. Recent probabilistic work includes boson point processes, exchangeability and random discrete structures such as random partitions, Gibbs random trees, random graphs and so on. Recent statistical work has focused on health monitoring and survival processes. Peter is the author of two books, Tensor Methods in Statistics, and Generalized Linear Models, with co-author John Nelder. He has served as editor of the journal Bernoulli, and as an associate editor of Biometrika, Journal of the Royal Statistical Society, and the Annals of the Institute of Statistical Mathematics.

**Dusa McDuff**(Stony Brook University)Dusa McDuff launched her career while she was a graduate student at Cambridge University (where she earned her Ph.D. in 1971) when she solved a well-known problem about von Neumann algebras, by constructing infinitely many different factors of type "II-one." After this, she had the opportunity to travel to Moscow where she had the good fortune to study with Israel M. Gel'fand, who taught her to view math as a kind of poetry and whose work greatly influenced her own. McDuff returned to Cambridge for a two-year Science Research Council Fellowship, before being appointed lecturer first at the University of York (1972-1976) and then at the University of Warwick (1976-1978). It was during her years at York and Warwick that McDuff realized some of the real difficulties involved in reconciling the demands of a career with her life as a woman. McDuff recalls feeling "very isolated" in a male-dominated field, and having to serve not only as the "family breadwinner" but also as "housekeeper and diaper changer" (her husband "said that diapers were too geometric for him to manage"). When McDuff was offered a visiting position at the Massachusetts Institute of Technology (1974-1975), she felt she was at a turning point in her career, realizing simultaneously that she was very far from being the kind of mathematician she felt she could be and that she could do something about it. She became in her own words "much less passive"--applying and getting into the Institute for Advanced Study, separating from her husband, delving into new mathematical problems concerning the relation between groups of diffeomorphisms and the classifying space for foliations, and publishing a joint paper with Graeme Segal on the Group Completion Theorem. Over the past twelve years, McDuff has worked on global symplectic geometry. This geometry is a structure on space that underlies many of the equations governing both classical and modern theories of Physics. Until recently, very little was known about it because there were no suitable tools with which to analyze it. McDuff has helped in the development of an understanding of its basic properties, and, together with Dietmar Salomon, has written a basic textbook on the subject. She has also remarried, to Jack Milnor, had a second child, and has been awarded numerous honors including the Satter Prize of the American Mathematical Society in 1991. Dusa McDuff was elected a Fellow of the Royal Society of London in 1994 and a member of the United States National Academy of Sciences in 1999. At the State University of New York at Stony Brook, where McDuff has been Professor of Mathematics since 1978, she has been a major participant in Calculus reform, and has been very active in the Women in Science and Engineering (WISE) program. This program offers academic, financial and social support to female undergraduate students in those fields.

**Robert Moody**(University of Victoria)

**David Mumford**(Brown University)David Bryant Mumford is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. He is currently a professor in the Division of Applied Mathematics at Brown University, having previously had a long academic career at Harvard University. At Harvard, Mumford became a student of Oscar Zariski, and his work in geometry always combined the traditional geometric insights with the latest algebraic techniques. He published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on the equations defining an abelian variety, and on algebraic surfaces. His books Abelian Varieties (with C. P. Ramanujam) and Curves on an Algebraic Surface combined the old and new theories (to the disadvantage of the former, it has been claimed by Shreeram Abhyankar). His lecture notes on scheme theory circulated for years in unpublished form, at a time when they were, beside the treatise Éléments de géométrie algébrique, the only accessible introduction. They are now available as The Red Book of Varieties and Schemes (ISBN 3-54-063293-X). Other work that was less thoroughly written up were lectures on varieties defined by quadrics, and a study of Shimura's many papers from the 1960s. Mumford’s research did much to revive the classical theory of theta functions, by showing that its algebraic content was large, and enough to support the main parts of the theory by reference to finite analogues of the Heisenberg group. He published some further books of lectures on the theory. He also was one of the founders of the toroidal embedding theory; and sought to apply the theory to Gröbner basis techniques, through students who worked in algebraic computation. He was awarded a Fields Medal in 1974. During the 1980s he left algebraic geometry, in order to study brain structure. He was a MacArthur Fellow from 1987 to 1992. In 2002, he wrote a book with Caroline Series and David Wright on the visual geometry of limit sets: Indra's Pearls: The Vision of Felix Klein. His current area of work is pattern theory.

**Robert Myers**(Perimeter Institute)Robert Myers is one of the leading theoretical physicists, working in the area of string theory in Canada. He received his Ph.D. at Princeton University in 1986, after which he was a postdoctoral researcher at the Institute for Theoretical Physics at the University of California, Santa Barbara. He moved to McGill University in 1989, where he was a Professor of Physics until moving to the Perimeter Institute and the University of Waterloo in the summer of 2001. Professor Myers is the 2005 winner of Canada's top prize in theoretical and mathematical physics awarded by the Canadian Association of Physicists and the Centre de Recherches Mathematiques. He was awarded the Herzberg Medal in 1999 by the Canadian Association of Physicists, for seminal contributions to our understanding of black hole microphysics and D-branes. He is one of only two people to have won the first award in Gravity Research Foundation Essay Contest twice (1997,1995). This contest was established for the purpose of stimulating thought and encouraging work on gravitation, and past winners in the fifty year history of this contest include Stephen Hawking and Roger Penrose. He is a fellow of the Cosmology and Gravity Program of the Canadian Institute of Advanced Research, a uniquely Canadian enterprise devoted to networking top-flight researchers from across the country. From 2001 to 2005, Professor Myers was a founding member on the scientific advisory board of the Banff International Research Station, a new facility devoted to hosting workshops and meetings in the mathematical sciences and their related areas. He is also an editor for the research journal, Annals of Physics. While his current activities are primarily centered at the new Perimeter Institute, Professor Myers remains active in both teaching and supervising graduate students with his cross appointment as a full professor in the Department of Physics at the University of Waterloo.

**Ken Ono**(Emory University)Ken Ono is the Solle P. and Margaret Manasse Professor of Letters and Science and the Hilldate Professor of Mathematics at the University of Wisconsin at Madison. After receiving his PhD in 1993 from UCLA, Ono held positions at the University of Illinois and the University of Georgia. He was a member of the Institute for Advanced Study for two years before moving to Penn State University, where he earned the title of Louis J. Martarano Professor of Mathematics before moving to Wisconsin. Ono has authored over 130 papers in Number Theory. He has received the NSF CAREER award, an Alfred P. Sloan Research Fellowship, the Presidential Early Career Award for Scientists and Engineers from President Clinton, a David and Lucile Packard Research Fellowship, an H. I. Romnes Fellowship, and a John S. Guggenheim Fellowship. In a ceremony at the National Academy of Sciences in Washington DC. in 2005, Ono was awarded the National Science Foundation Director's Distinguished Teaching Scholar Award, the highest honor bestowed by the NSF for excellence in research and education.

**Hirosi Ooguri**(California Institute of Technology)After receiving B.A. in 1984 and M.S. in 1986 from Kyoto University, Ooguri became an Assistant Professor with tenure at the University of Tokyo in 1986. He was a research associate at the Institute for Advanced Study in Princeton from 1988 to 1989. He received Sc.D. from the University of Tokyo in 1989. Subsequently, Ooguri held faculty appointments at the University of Chicago and at the Research Institute for Mathematical Sciences in Kyoto University. In 1994, he became a Professor at the University of California at Berkeley and was appointed a Faculty Senior Scientist at the Lawrence Berkeley National Laboratory in 1996. Since 2000, he has been at Caltech, where he is now Fred Kavli Professor of Theoretical Physics. In 2007, he also became a principal investigator of the newly established Institute for the Physics and Mathematics of the Universe at the University of Tokyo. Ooguri, together with Andrew Strominger and Cumrun Vafa, received the inaugural Leonardo Eisenbud Prize for Mathematics and Physics from the American Mathematical Society in 2008, for the work relating the counting of black hole microstates to the Gromov-Witten invariants. He has been chosen to receive a Humboldt Research Award from the Alexander von Humboldt Foundation. In 2008, he gave the Takagi Lectures of the Mathematical Society of Japan. Ooguri is a member of the Aspen Center for Physics and is on the advisory board of the International Solvay Institute in Brussels. Previously, he was a member of the Advisory Board of the Kavli Institute for Theoretical Physics in Santa Barbara. He is an editor of Physical Review D and is a supervisory editor of Nuclear Physics B. He has held visiting appointments at Harvard University and at the University of Paris VI, and was a 21st Century Center of Excellence Visiting Professor at the University of Tokyo in 2007.

**Irena Peeva**(Cornell University)Irena Peeva obtained her Ph.D. in 1995 from Brandeis University under the guidance of David Eisenbud. After holding a C.L.E. Moore Instructorship at M.I.T., she joined the faculty of Cornell University in 1998. Her research interests are in Commutative Algebra and its connections to Algebraic Geometry, Combinatorics, Computational Algebra, Subspace Arrangements, and Noncommutative Algebra, with special emphasis on Free Resolutions, Hilbert Schemes and Hilbert Functions. She is the author of the book Graded Syzygies, published by Springer. Peeva was invited to deliver a Plenary Address at the National Meeting of the AMS (generally known as the Joint Mathematics Meeting) in 2015 and a Plenary Address at the CMS Summer Meeting in 2013. She received a Sloan Doctoral Dissertation Fellowship (1994/1995), C.L.E. Moore Instructorship at M.I.T. (1995-1998), Sloan Foundation Fellowship (1999-2001), NSF CAREER Grant (2004-2009), Simons Foundation Fellowship (2012/2013), and is an AMS Fellow since 2013.

**Yuval Peres**(Microsoft Research)Yuval Peres is currently the manager of the Theory Group at Microsoft Research, Redmond, and is also affiliated with the University of Washington and the University of California, Berkeley. Yuval graduated from the Hebrew University, Jerusalem in 1990. He has taught at Stanford, at Yale and in Jerusalem, and was a Professor at UC Berkeley until 2006. He is a recipient of the Ben Porath, Rollo Davidson and Loeve prizes and was an invited speaker at the International Congress of Mathematicians in Beijing, 2002. Yuval works on random walks, Brownian motion, Mixing of Markov chains, Hausdorff dimension percolation, random spanning trees, point processes and random analytic functions. He enjoys collaborating with Students and Postdocs. His favourite conference venue is the Banff Research station and his favourite quote is from his son Alon, who was overheard at age 6 asking a friend: "Leo, do you have a religion? You know, a religion, like Christian, or Jewish, or Mathematics....?"

**Victor Perez-Abreu**(Centro de Investigacion en Matematicas)Victor Pérez-Abreu is a researcher in the Probability and Statistics Department of the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. In 1977 he received his BS in Physics and Mathematics from the National Polytechnic Institute in Mexico City, and in 1985 his Ph. D. from University of North Carolina at Chapel Hill. He joined CIMAT in 1986 and has served as Chair of the Department of Probability and Statistics during several periods. From 1997 to 2003 he was General Director of CIMAT. He is a Fellow of the Institute of Mathematical Statistics and was President of the Bernoulli Society for Probability and Mathematical Statistics. His research interests multiple Wiener-Ito integrals and chaos expansions, as well as stochastic processes on duals of nuclear Fréchet spaces. Past projects involved the use of empirical generating function and other characteristics to construct goodness of fit tests for discrete and some scale distributions. More recently, his interests have been in Lévy processes and infinitely divisible aspects of random matrices and distributions on cones, and infinite divisibility in the free sense and other kinds of convolutions.

**Ed Perkins**(UBC)Dr. Edwin Perkins is Professor of Mathematics at the University of British Columbia where he was first appointed as a postdoctoral fellow in 1979. He did is his undergraduate degree at U. of Toronto and obtained his doctoral degree from the U. of Illinois. His research interests in probability include the general theory of processes, Brownian motion, stochastic differential equations and partial differential equations, interacting particle systems, measure-valued diffusions and stochastic models in population genetics. He has won numerous awards for his research including the Coxeter-James Lectureship (1986), G. de B. Robinson Award (1996) and Jeffery-Williams Prize (2002) (Canadian Math. Society), the Rollo Davidson Prize (1983) (Cambridge U.) and a Steacie Fellowship (1992-93) (NSERC). He is a Fellow of the Royal Society of Canada and the Institute of Mathematical Statistics and presently sits on the editorial Boards of the Annales de l’Institut Henri Poincare, Stochastic Processes and Their Applications and the Electronic Journal of Probability. He has given several invited lectureships including an invited address at the 1994 International Congress of Mathematicians in Zurich.

**Arturo Pianzola**(University of Alberta)Arturo Pianzola received his PhD in 1984 under the supervision of Robert Moody. He specializes in applications of Galois cohomology, descent formalism, and the Demazure-Grothedieck theory of reductive group schemes to the study of problems in infinite dimensional Lie theory. He has been awarded a McCalla and a Killam Professorship, and has also been and Invited Professor at Universite Paris-Sud and Ecole Normale Superieure. He is a Professor of Mathematics at the University of Alberta and "Investigador Principal" of CONICET.

**Nicholas Pippenger**(Princeton University)Nick is Professor of Computer Science at Princeton University. Before coming to Princeton, he worked for the MIT Instrumentation Laboratory (now the Charles Stark Draper Laboratory), IBM Research, and the University of British Columbia. He received the B.S. in Natural Science from Shimer College in 1965, and the B.S., M.S. and Ph.D. in Electrical Engineering from MIT in 1967, 1969 and 1974. His research interests center in theoretical computer science, but also extend into communication theory and mathematics. Nick is a Fellow of the Royal Society of Canada (Academy of Science), a Fellow of the ACM (Association for Computing Machinery) and a Fellow of the IEEE (Institute of Electrical and Electronics Engineers). He is also a member of the AMS (American Mathematical Society), the MAA (Mathematical Association of America) and SIAM (Society for Industrial and Applied Mathematics). He is the author of Theories of Computability, published by Cambridge University Press in 1997.

**Gilles Pisier**(Texas A & M University)Gilles Pisier holds the A.G & M.E. Owen Chair and is Distinguished Professor of Mathematics at Texas A& M University, and is Professeur Emerite at Université Paris VI. He has published over 150 papers, 7 books and has served on many editorial boards: Astérisque, Annales Institut Henri Poincaré, Probabilités-Statistiques, Bulletin des Sciences Mathématiques, Houston J. Math., Annals of Probability, Geometric and Functional Analysis, Math. Ann., Advances in Math, Operator Theory, Proc. Edinburgh Math. Soc., Duke Math. J., J. Functional Analysis. He has won many honors and awards, among them the following: Salem prize, 1979, Cours Peccot au Collège de France, 1981, Prix Carrière de l’Académie des Sciences de Paris, 1982, Invited address, International Congress of Mathematicians, 1983, Fellow of the Institute of Mathematical Statistics, 1989, Grands prix de l’Académie des Sciences de Paris: Prix Fondé par l’Etat, 1992, Elected “Correspondant” (April 1994), then Member (Nov. 2002) of “Académie des sciences de Paris,” Ostrowski prize 1997, Invited speaker, Plenary talk, ICM Berlin 1998, Stefan Banach medal (Polish Academy of Science) 2001, Foreign Member of Polish Academy of Science 2005, and Indian National Science Academy.

**Daniel Pollack**(University of Washington)Daniel Pollack received his BS and MS from the University of Pennsylvania in 1986 and his PhD from Stanford University in 1991. After post-doctoral positions at the University of Texas Austin and the Mathematical Sciences Research Institute he spent two years as an Assistant Professor at the University of Chicago before moving to the University of Washington in 1996 where he is currently a Professor of Mathematics. His research interests include problems at the interface of differential geometry and partial differential equations. For the last ten years the focus of his work has been centered on mathematical problems in general relativity, and he is a co-author (along with Piotr Chrusciel and Gregory Galloway) of a major survey of the field which appeared in the Bulletin of the AMS in 2010. He has held visiting appointments at IAS, Brown, MIT, MSRI, the Newton Institute and Institute Mittag-Leffler. His research is currently supported by the Simons Foundation.

**Mary Pugh**(University of Toronto)Mary Pugh is a professor of mathematics at the University of Toronto at St George. She received her B.A. in pure mathematics from the University of California at Berkeley in 1986 and her M.S. and Ph.D. in mathematics from the University of Chicago in 1988 and 1993, respectively. Since then, she has held various positions at the Courant Institute of New York University (1993-94, 1995-97), the Institute for Advanced Study (1994-95), and the University of Pennsylvania (1997-2001). She received a Sloan Fellowship in 1997. She is on the editorial board of the European Journal of Applied Mathematics and Discrete and Continuous Dynamical Systems, Series B. Her research area is in applied mathematics, including nonlinear PDE, fluid dynamics, mathematical biology, and scientific computation.

**Ian Putnam**(University of Victoria)His main area of research interest is in the interaction between C*-algebras and topological dynamics. He is interested in the structure of C*-algebras which may be constructed from dynamical systems and also the information about the dynamics which is available by studying these C*-algebras. In particular, his interests include: Cantor minimal systems, hyperbolic systems, symbolic dynamics, aperiodic tilings, K-theory of C*-algebras, dimension groups, groupoids and groupoid C*-algebras.

**Sujatha Ramdorai**(University of British Columbia)Sujatha Ramdorai had her early education in India and obtained her Ph.D in Tata Institute of Fundamental Research/Bombay University. She is a Fellow of all the three Science Academies in India and is a recepient of the Shansti Swarup Bhatnagar Award, and the ICTP Ramanujan Award. She served as a member of the National Knowledge Commission, Government of India between 2007-2009. She is a member of several international Scientific Research committees, like IFCPAR (Indo-French centre for Promotion of Advanced Research), CIMPA (International Centre for Pure and Applied Mathematics), ICTS (International Centre for Theoretical Sciences, India). She currently holds a CRC position at the University of British Columbia, Vancouver.

**James Ramsay**(McGill University)Jim Ramsay is a Professor Emeritus of Psychology and an Associate Member in the Department of Mathematics and Statistics at McGill University. He received a Ph.D. from Princeton University in 1966 in quantitative psychology. He served as chair of the Department from 1986-1989. Jim has contributed research on various topics in psychometrics, including multidimensional scaling and test theory. His current research focus is on functional data analysis, and involves developing methods for analyzing samples of curves and images. The identification of systems of differential equations from noisy data plays an important role in this work. He has been President of the Psychometric Society and the Statistical Society of Canada. He received the Gold Medal of the Statistical Society of Canada in 1998 and the Award for Technical or Scientific Contributions to the Field of Educational Measurement of the U. S. National Council on Measurement in Education in 2003, and was made an Honorary Member of the Statistical Society of Canada in 2012.

**Alexander Razborov**(University of Chicago)Alexander Razborov graduated from the Moscow State University (Department for Mathematics and Mechanics) in 1985 and in the same year entered the graduate school of Steklov Mathematical Institute of the Russian Academy of Sciences. He defended his PhD thesis in 1987 and joined the Steklov faculty, where he has been working since then. In 1990 he was awarded the Nevanlinna prize by the International Mathematical Union. He has been a member of Academia Europea since 1993, and a corresponding member of the Russian Academy of Sciences since 2000. For the period 2000-2008 he is holding a visiting position at the Institute for Advanced Study, Princeton (School of Mathematics).

**Zinovy Reichstein**(University of British Columbia)Zinovy Reichstein received his Ph.D. degree from Harvard in 1988, under the direction of Michael Artin. After holding postdoctoral positions at the University of Pennsylvania, UC Berkeley, and MSRI, he has been on the faculty at Oregon State University (1993-2001) and the University of British Columbia (since 2001), He served as Associate Head of the UBC Mathematics Department in 2009-10. Reichstein received a Faculty Award for Excellence in Teaching at Oregon State University in 1997 and was an invited speaker at the International Congress of Mathematicians in Hyderabad in 2010. Reichstein's Ph.D. work was in geometric invariant theory, an area of algebraic geometry concerned with the construction and study of moduli spaces. His interests have since expanded to a number of other fields within algebra, algebraic geometry, and the theory of algebraic groups; he also occasionally ventures into adjacent areas of algebraic combinatorics, computational algebra, number theory and algebraic topology. He has published 60 research papers and is best known for his work on numerical invariants of algebraic groups, such as essential and canonical dimension.

**Nancy Reid**(University of Toronto)Nancy Reid is University Professor of Statistics at the University of Toronto. She received her Bachelor of Mathematics in 1974 from the University of Waterloo, her MSc in 1976 from the University of British Columbia, and her Ph.D. in 1979 from Stanford University. She held an academic appointment at the University of British Columbia from 1980-1986 and has held visiting appointments at Imperial College, London, Harvard University and the University of Texas at Austin. She is a former vice-president of the International Statistical Institute, and a former President of the Institute of Mathematical Statistics. She is a fellow of the American Statistical Association and the Institute of Mathematical Statistics, a recipient of the Presidents' Award of the Committee of Presidents of Statistical Societies, the first recipient of the Canadian Mathematical Society's Krieger-Nelson Prize Lectureship, and the Institute of Mathematical Statistics' Wald lecturer for 2000. Her research interests include inferential statistics with special emphasis on asymptotic theory for likelihood based inference, design of experiments, and applications of statistics to health and environment.

**Walter Schachermayer**(University of Vienna)Walter Schachermayer is Professor of Mathematics at the University of Vienna. His research is concerned with stochastic processes and their applications in finance. Professor Schachermayer held positions at the University of Linz and the Technical University Vienna. Walter Schachermayer was the first Austrian mathematician to receive the Wittgensteinpreis (1998). He is a member of the German National Academy of Science Leopoldina and European Academy of Science. Professor Schachermayer holds an honorary doctorate from Universite Paris Dauphine. In 2009 he was awarded an ERC Advanced Grant. Among his achievements is the proof of the "Fundamental Theorem of Asset Pricing" in its general form, which was done in joint work with Freddy Delbaen.

**Dominik Schoetzau**(University of British Columbia)Dominik Schötzau is currently a Canada Research Chair and Professor of Mathematics at the University of British Columbia. He received his MSc and PhD degree from the Swiss Federal Institute of Technology (ETH) in Zurich, and held a postdoctoral position at the University of Minnesota. Before moving to UBC in 2003, he worked as an Assistant Professor at the University of Basel in Switzerland. His research is primarily in the areas of Computational Mathematics and Scientific Computation, with applications in Fluid Mechanics and Electromagnetics.

**José Antonio Seade Kuri**(Universidad Nacional Autonoma de Mexico)Jose Seade was born in Mexico City in 1954. He got his BSc degree in Mathematics at the Universidad Nacional Autonoma de Mexico (UNAM) in 1976, and then his Master’s (1977) and Ph. D. degrees (1980) at the University of Oxford, U. K.. He has worked at the Institute of Mathematics of UNAM since 1980. His main research contributions are in singularity theory, real and complex foliations and complex geometry. He was President of the Mexican Mathematical Society during 1996-1997, and in 2005 he was awarded the Ferran Sunyer I Ballaguer Prize for his monograph “On the topology of isolated singularities in Analytic Spaces”. He was a Staff Associate at the International Centre of Theoretical Physics in Trieste, Italy, during 2005-2011, and a member of the Scientific Committee of the Latin American Union of Mathematicians (UMALCA) during 2001-2009. He is currently a member of the Steering Committee of the Pacific Rim Mathematical Association (PRIMA) and Scientific Coordinator of the Solomon Lefschetz International Laboratory (LAISLA), associated to the CNRS (France) and CONACYT (Mexico).

**Gordon Semenoff**(University of British Columbia)Gordon Semenoff is a theoretical physicist and is Professor of Physics at the University of British Columbia. His research spans a wide range of theoretical subjects from condensed matter physics to string theory. He was awarded the CAP/CRM Prize in Theoretical and Mathematical Physics year 2000 and the Brockhouse Medal for Achievement in Condensed Matter Physics and Material Science in 2010. He was also awarded the Canadian Association of Physicists Medal for Lifetime Achievement in Physics in 2011. He is a Fellow of the Royal Society of Canada and an Officer of the Order of Canada. Gordon received his Ph.D. from the University of Alberta in 1981, was a postdoctoral Fellow at the Massachusetts Institute of Technology and joined the faculty of the University of British Columbia in 1983. He has held visiting professorships at numerous institutions worldwide including the Institute for Advanced Study in Princeton, the Niels Bohr Institute in Copenhagen, the Henri Poincare Institute in Paris and the Institut des Hautes Etudes Scientifiques in Bures-Sur-Yvette. Gordon has achieved international recognition for his 1984 pioneering work on the substance which later became known as graphene. His highly cited work which predated the discovery of graphene in the laboratory by 20 years was important for understanding that material and its remarkable electronic properties which have generated considerable excitement in fields spanning condensed matter physics, material science and electronics technology. Gordon is well known for contributions to quantum field theory, in particular for using mathematical index theorems to understand fractional charges and the discovery of the parity anomaly of odd-dimensional gauge theories. These ideas have had significant influence over the years and have recently come to the forefront in studies of topological insulators. His pioneering work on the real-time formulation of relativistic quantum field theories at non-zero temperature and density, including invention of the “Kobes-Semenoff rules”, are considered cornerstones of that subject. He has made important contributions to string theory. His computation of the Wilson loop in N = 4 Yang Mills theory is considered a classic and an important test of a duality between gauge fields and strings. His pioneering work in 2002 on string loop corrections to plane wave strings is considered seminal, not just for its results, but as the beginning of the integrability program of supersymmetric gauge theory and string theory which has been widely pursued over the ten years since.

**Gadiel Seroussi**(MSRI)Gadiel Seroussi is Director of Information Theory Research at Hewlett-Packard Laboratories. He received the B.Sc. degree in electrical engineering, and the M.Sc. and D.Sc. degrees in computer science from Technion -- Israel Institute of Technology, Haifa, Israel, in 1977, 1979 and 1981, respectively. From 1981 to 1987, Seroussi was with the faculty of the Computer Science Department at Technion. During the 1982-83 academic year, he was a Postdoctoral Fellow at the Mathematical Sciences Department of IBM T.J. Watson Research Center, Yorktown Heights, New York. From 1986 to 1988, he was a Senior Research Scientist with Cyclotomics Inc., Berkeley, California. He joined Hewlett-Packard Laboratories in Palo Alto, California, in 1988. Since 2004, he also holds an honorary full professor appointment in Computer Science and Electrical Engineering at Universidad de la RepÃƒÂºblica in Montevideo, Uruguay. His research interests include the mathematical foundations and practical applications of information theory, error correcting codes, data and image compression and cryptography. Dr. Seroussi is a Fellow of the IEEE, cited "for contributions to the theory and practice of error correction and data compression algorithms and architectures." His algorithmic contributions to error correction coding systems have had a significant impact on the present methodologies and state of the art in Reed-Solomon codec design. He is a co-inventor of the algorithm at the core of the JPEG-LS lossless image compression standard. This algorithm is being used by the NASA Mars rovers for lossless transmission of images from Mars. He has also contributed to the coding algorithm of the JPEG-2000 standard. Dr. Seroussi has published numerous journal and conference articles in his areas of expertise, is a co-author of the book "Elliptic Curves in Cryptography," published by Cambridge University Press (a preferred reference for theoreticians and practitioners in this area), and a co-editor of the sequel "Advances in Elliptic Curve Cryptography," published by Cambridge in 2005. He is an inventor on 23 granted U.S. patents, and more than 40 pending patents and invention disclosures.

**Gordon Slade**(University of British Columbia)Gordon Slade received his PhD in mathematics from the University of British Columbia in 1984. He spent two years at the University of Virginia before moving to McMaster University from 1986 to 1999. Since 1999 he has been a professor of mathematics at the University of British Columbia. His research interests are in probability theory and statistical physics. He is best known for his development of the lace expansion to solve many problems in the area. Gordon Slade has served on scientific panels for the Fields Institute, PIMS, NSERC, and the Royal Society of Canada. He gave an Invited Lecture at the International Congress of Mathematicians in 1994, received the Coxeter-James award of the Canadian Mathematical Society in 1995, was elected Fellow of the Royal Society of Canada in 2000, received the Prix de l'Institut Henri Poincare in 2003, and was awarded a Killam Research Prize in 2004.

**Karen Smith**(University of Michigan)Karen Smith received her PhD from the University of Michigan in 1993. After holding an NSF post-doctoral fellowship at Purdue University, and a Moore Instructorship and Assistant Professorship at MIT, she eventually returned to Michigan as a professor, where she remains today. She was awarded a Sloan Fellowship in 1997, a Fulbright Fellowship in 2001 (in Jyvaskyla, Finland), and various other awards for her teaching and research. She has served as editor or associate editor for six mathematical journals, and also as member of the National Research Council's Board of Mathematical Sciences. Smith's main research areas are commutative algebra and algebraic geometry. In 2001, she was awarded the American Mathematical Society's Satter prize for her work on tight closure and its applications to algebraic geometry.

**Panagiotis Souganidis**(University of Chicago)Panagiotis Souganidis has been a Professor at the University of Texas at Austin since 2001. He received his PhD from the University of Wisconsin-Madison under the supervision of M. G. Crandall. Before Texas he held faculty positions at Brown University and the University of Wisconsin-Madison. He is the recipient of a Sloan Fellowship, a Presidential Young Investigator Award and a Bodossaki Foundation Academic Prize. In 1994 he gave an invited talk at the ICM in Zurich. Souganidis works on nonlinear partial differential equations and stochastic analysis with emphasis on nonlinear elliptic equations, Hamilton-Jacobi equations and stochastic partial differential equations.

**Douglas Stinson**(University of Waterloo)Douglas Stinson obtained his PhD from the University of Waterloo in 1981. He previously has held academic positions at the University of Manitoba, where he was an NSERC University Research Fellow, and the University of Nebraska-Lincoln. Currently he holds the position of University Research Chair in the School of Computer Science at the University of Waterloo. Doug held the NSERC/Certicom Industrial Research Chair in Cryptography from 1998-2003. Doug's research interests include cryptography and computer security, combinatorics and coding theory, and applications of discrete mathematics in computer science. Doug is the author of over 200 research papers as well as the popular textbook "Cryptography: Theory and Practice", the third edition of which was published in 2005. He was one of the founding co-editors of the Journal of Combinatorial Designs, which is published by John Wiley & Sons, and he has served on the editorial boards of numerous other journals. Doug is currently the Chair of the Selected Areas in Cryptography (SAC) Organizing Board. SAC is a leading cryptography workshop that has been held annually in Canada since 1994.

**Benny Sudakov**(ETH - Zurich)Benny Sudakov got his Ph.D from Tel Aviv University in 1999, had appointments in Princeton University and Institute for Advanced Studies and is currently professor of mathematics in ETH, Zurich and UCLA. He is the recipient of an Alfred P. Sloan Foundation Fellowship, an NSF CAREER Award and was invited speaker at 2010 International Congress of Mathematicians. His main research interests are Combinatorics and its applications to other areas of mathematics and computer science.

**Elizabeth Thompson**(University of Washington)Elizabeth Thompson received a B.A. in Mathematics (1970), a Diploma in Mathematical Statistics (1971), and Ph.D. in Statistics (1974), from Cambridge University. In 1974-5 she was a NATO/SRC post-doc in the Department of Genetics, Stanford University. From 1975-81 she was a Fellow of King's College, Cambridge, and from 1981-5 was Fellow and Director of Studies in Mathematics at Newnham College. From 1976-1985 she was a University Lecturer in the Department of Pure Mathematics and Mathematical Statistics, University of Cambridge. She joined the faculty of the University of Washington in December 1985, as a Professor of Statistics. She is also an Adjunct Professor in the Departments of Biostatistics and of Genome Sciences at the University of Washington. She served as Chair of the Department of Statistics from 1989-94 and from 2011-14. In 1981, she was elected a member of the International Statistical Institute, and in 1988, she was awarded an Sc.D. degree by the University of Cambridge. In 1994, she gave the R.A. Fisher Lecture at the Joint Statistical Meetings in Toronto. In 1996, she gave the Neyman Lecture (IMS) at the Joint Statistical Meetings in Chicago. In 1998, she was elected a Fellow of the American Academy of Arts and Sciences. In 2001, she received the inaugural Jerome Sacks Award for Cross-Disciplinary Research from the National Institute for Statistical Science, and was also awarded the Weldon Prize, an international prize for contributions to Biometric Science awarded by the University of Oxford. She has held a Guggenheim Fellowship, and has been a Rothschild Visiting Professor at the University of Cambridge and a Carnegie Centenary Visiting Professor at the University of St Andrews. In 2008 she was elected to the US National Academy of Sciences. She served as President of the International Biometric Society in 2016 and 2017. Dr. Thompson's research interest is in the development of methods for inference from genetic data, and particularly from patterns of genome sharing observed among members of large and large and complex pedigree structures, whether of plants, animals, or humans. Questions of interest range from human genetic linkage analysis to gene extinction in highly endangered species, and from inference of relationship to inferences of the genetic basis of traits, Her current focus is on developing research and education in Statistical Genetics at the University of Washington.

**Gang Tian**(Princeton University)Professor Tian is the Simons Professor of Mathematics at the Massachusetts Institute of Technology. While at UBC, he will lecture on Recent Progress in Complex Geometry. Professor Tian's research covers such diverse areas as differential geometry, algebraic geometry, geometric analysis and partial differential equations. He has made fundamental contributions in each of these areas. In particular, he is well known for his work on the question of existence and obstructions for Kähler-Einstein metrics on complex manifolds with positive first Chern class, for his proof that the qantum cohomolgy ring is associative (joint with Y. Ruan) and for his work on higher dimensional dimensional gauge theory. Tian received the 19th Alan Waterman Award from the National Science Foundation in 1994, the Oswald Veblen Prize in 1996 and was an Alfred P. Sloan Research Fellow from 1991-93. He has been invited to give many prestigious lectures around the world. A partial list includes the International Congress of Mathematicians in Kyoto (1990), the Bergmann Memorial Lecture at Stanford University (1994), the Courant Lecture at New York University (1996), Distinguished Visiting Lectures at the University of Wisconsin (1996), Nachdiplomvorlesung Lectures at ETH, Zürich (1997), Myhill Lectures at New York State University, Buffalo (1998) and the Andrejewski Lectures at Göttingen University (1999).

**Rob Tibshirani**(Stanford University)Rob Tibshirani is the Associate Chairman and Professor of Health Research and Policy, and Statistics at Stanford University.

**Nicole Tomczak-Jaegermann**(University of Alberta)Nicole Tomczak-Jaegermann received her Ph.D. from the Warsaw University, Poland. In 1983 she came to Canada and took a position at the University of Alberta, Edmonton. She is working in Banach Space Theory, in particular she is interested in finite-dimensional spaces and properties of Banach spaces which depend on the structure of their finite-dimensional subspaces. Alone and with collaborators, she has solved several problems in her area open at least from the 60's. In particular, her work constitutes an essential ingredient in a recent solution by the 1998 Fields Medallist W. T. Gowers, of the homogeneous space problem raised by Banach in 1932. Her most recent interests are in asymptotic geometric analysis, concerned with geometric and linear properties of finite-dimensional objects, especially with asymptotics of their various quantitative parameters as the dimension tends to infinity, studied by deep geometric, probabilistic and combinatorial methods. Tomczak-Jaegermann was elected an FRSC in 1996, awarded the Canada Council Killam Research Fellowship in 1997/99, and was invited to give a lecture at the International Congress of Mathematicians in Berlin in 1998. In 2001 she was appointed Canada Research Chair in Geometric Analysis.

**Nizar Touzi**(Ecole Polytechnique)- Professor Ecole Polytechnique - PhD, University Paris Dauphine 1994, Habilitation University Paris Dauphine 1999 - Vice President, Bachelier Society - Co-editor, Finance and Stochastics, Paris-Princeton Lectures on Mathematical Finance - Associate Editor, Mathematical Finance, Electronic Journal of Probability, SIAM Journal on Financial Mathematics - Europlace Institute of Finance Best Young Researcher Award 2006 - University of Toronto Dean's Distinguished Visitor Chair 2010 - Invited Session Speaker ICM 2010

**Richard Tsai**(University of Texas at Austin)

**Gunther Uhlmann**(University of Washington)Gunther Uhlmann was born in Quillota, Chile. He received his Licenciatura degree at the University of Chile in 1973 and the PhD at MIT in 1976 under the direction of Victor Guillemin. After postdoctoral positions at Harvard University, Courant Institute and MIT he became Assistant Professor at MIT in 1980. He moved to the University of Washington in 1985 and became Full Professor in 1987. He is a Sloan and Guggenheim Fellow, and was an invited speaker at the International Congress of Mathematics in Berlin in 1998 and a plenary speaker at the International Congress of Industrial and Applied Mathematics in Zurich in 2007. His current main interest is inverse problems, in particular inverse boundary value problems and inverse scattering problems. In these problems, one attempts to determine internal parameters of a medium by making measurements at the boundary of the medium or by remote observations. He is a member of the American Academy of Arts & Sciences.

**Alberto Verjovsky**(UNAM Mexico)Alberto Verjovsky was born in Mexico City on January 2, 1943. He did his BSc in Mathematics at the Universidad Nacional Autonoma de Mexico (UNAM) in 1962 and wrote an honors thesis under the supervision of Solomon Lefschetz. He obtained his PhD degree at Brown University in 1973 and was full professor at CINVESTAV (Centro de Investigacion y Estudios Avanzados del Instituto Politecnico Nacional) from 1973 to 1986. From 1986 to 1993 he was coordinator of the Mathematics Section of the International Centre for Theoretical Physics at Trieste, Italy. From 1993 to 2008 he was full professor at the Universite des Science et Technologies de Lille, France. From 2008 to the present day he is full professor at the Instituto de Matematicas de la UNAM in the city of Cuernavaca, Mexico.

**Jeff Viaclovsky**(University of Wisconsin)Jeff Viaclovsky is Professor of Mathematics at the University of Wisconsin Madison, and his research interests involve differential geometry and geometric analysis. He received his Ph.D. in 1999 from Princeton University, and held appointments at the University of Texas at Austin and Massachusetts Institute of Technology, before moving to Madison in 2006. He held an NSF Postdoctoral Fellowship from 1999-2002, an Alfred P. Sloan Foundation Research Fellowship from 2004-2006, and was a Simons Fellow in Mathematics in 2012-2013.

**Cédric Villani**(l'Institut Henri Poincaré)Cedric Villani was born in 1973 in France. After studying mathematics at Ecole Normale Superieure in Paris from 1992 to 1996, he was appointed assistant professor there. His 1998 PhD was mainly focused on the mathematical theory of the Boltzmann equation. Besides his advisor Pierre-Louis Lions (Paris-Dauphine), during his training he was much influenced by Yann Brenier, Eric Carlen and Michel Ledoux. In 2000 he became a full professor at l'Ecole Normale SupÃ©rieure de Lyon, and has stayed with that organization since then. He held semester-long visiting positions in Atlanta (1999), Berkeley (2004) and Princeton (2009), wrote about 50 research papers, and two reference books on optimal transport theory.

A mathematical analyst, Villani is particularly interested in fluid mechanics, statistical physics, probability, functional inequalities and Riemannian geometry.

His awards include the Jacques Herbrand Prize of the French Academy of Science (2007), the Prize of the European Mathematical Society (2008), the Henri Poincare Prize of the International Association for Mathematical Physics, the Fermat Prize (2009), and the Fields Medal (2010). His collaborators include Luigi Ambrosio, Dario Cordero-Erausquin, Laurent Desvillettes, Alessio Figalli, Wilfrid Gangbo, Gregoire Loeper, John Lott, Clement Mouhot, Ludovic Rifford, Giuseppe Toscani, and many others. He serves on the editorial boards of Inventiones Mathematicae, Journal of Functional Analysis, Journal of Mathematical Physics and Journal of Statistical Physics.

In 2009 he was appointed director of the Institut Henri Poincare (IHP) in Paris, and part-time visitor of the Institut des Hautes Etudes Scientifiques (IHES).

**Michael Vogelius**(Rutgers University)

**Michael Ward**(University of British Columbia)Michael Ward has been a Professor at the University of British Columbia (UBC) since 1998. He received his Ph.D in Applied Mathematics from Caltech in 1988, after first receiving his B.Sc from UBC in 1983. Prior to returning to UBC in 1993 as an Assistant Professor, Ward was a Szego Postdoctoral Fellow at Stanford from 1988-1991, and was a Postdoc at the Courant Institute from 1991-1993. His awards include the Andre-Aisendtadt Prize from the CRM in 1995, the Coxeter James Research Prize awarded by the CMS in 1997, the E.W.R. Steacie Memorial Fellowship awarded by NSERC in 1998, and the CAIMS Research Prize awarded by the Canadian Applied and Industrial Mathematics Society in 2011. In 1995 he gave an invited plenary lecture at the International Congress of Industrial and Applied Mathematics in Hamburg, Germany. He has been a Co-Editor-In-Chief of the European Journal of Applied Mathematics since 2001. He was the Director of the Institute for Applied Mathematics at UBC from 20003-2008. He has held various visiting positions, most notably at Oxford University as a Christiansen Research Fellow and at the Chinese University of Hong Kong. His main research interests relate to the study of the dynamics and stability of interfaces and other localized structures that occur in reaction-diffusion systems, in models of micro-electrical mechanical systems, and in the study of diffusive transport in various cell-signalling problems in mathematical biology.

**Michael Waterman**(University of Southern California)Michael Waterman holds an Endowed Associates Chair at USC. He came to USC in 1982 after positions at Los Alamos National Laboratory and Idaho State University. His bachelors in Mathematics is from Oregon State University, and his PhD in Statistics and Probability is from Michigan State University. He was named a Guggenheim Fellow (1995), was elected to the American Academy of Art and Sciences (1995), and was elected to the National Academy of Sciences (2001) . Also he is a Fellow of the American Association for the Advancement of Science and Fellow of the Institute of Mathematical Statistics. He has held visiting positions at the University of Hawaii (1979-80), the University of California at San Francisco (1982), Mt. Sinai Medical School (1988), Chalmers University (2000), and in 2000-2001 he held the Aisenstadt Chair at University of Montreal. He is Professor-at-large at the Keck Graduate Institute of Life Sciences and in fall 2000 he became the first Fellow of Celera Genomics. In 2002 he received a Gairdner Foundation International Award. Professor Waterman works in the area of Computational Biology , concentrating on the creation and application of mathematics, statistics and computer science to molecular biology, particularly to DNA, RNA, and protein sequence data. He is the co-developer of the Smith-Waterman algorithm for sequence comparison and of the Lander-Waterman formula for physical mapping. He is a founding editor of Journal of Computational Biology , is on the editorial board of seven journals, and is author of the text Introduction to Computational Biology: Maps, Sequences and Genomes.

**Peter Winkler**(Dartmouth College)Peter Winkler is Director of Fundamental Mathematics Research at Bell Labs, Lucent Technologies. For the academic year '03-'04 he is on sabbatical at the Institute for Advanced Study. A winner of the Mathematical Association of America's Lester R. Ford Award for mathematical exposition, Dr. Winkler is the author of about 125 mathematical research papers and holds a dozen patents in computing, cryptology, holography, optical networking and marine navigation. His research papers are primarily in combinatorics, probability and the theory of computing, with forays into statistical physics. Dr. Winkler received his BA from Harvard summa cum laude in mathematics, then after a stint in the US Navy, his PhD from Yale as a student of Abraham Robinson and Angus Macintyre. He joined the faculties of Stanford and then Emory University, where he became Professor and Chairman of Mathematics and Computer Science. In 1989 he left academia for industry, first Bellcore and then Bell Labs. When not proving theorems or enjoying his family, Winkler is generally found on a squash court or playing and composing ragtime piano music. In some circles he is best known as the inventor of cryptologic techniques for the game of bridge, which have now been declared illegal for tournament play in most of the western world.

**Daniel Wise**(McGill University)Dani Wise grew up in NY and received his BA from Yeshiva in 1991 and PhD from Princeton in 1996. After postdocs and visiting positions at Berkeley, Cornell, and Brandeis, he moved to McGill in 2001, where he is currently James McGill Professor. His primary research agenda has been to explore and promulgate the utility and ubiquity of nonpositively curved cubical geometry in group theory and topology. He received the Oswald Veblen prize in 2013, became a fellow of the Royal Society of Canada in 2014, spoke at the ICM in 2014, was Poincare Chair at the IHP in 2015, and received the CRM-Fields-PIMS Prize in 2016.

**Margaret Wright**(New York University)Margaret Wright received her B.S. in Mathematics and M.S. in Computer Science from Stanford University. After several years in industry, she returned to Stanford to complete her Ph.D. in Computer Science in 1976. Her thesis was on "Numerical Methods For Nonlinearly Constrained Optimization." She remained at Stanford as a Research Associate until joining Bell Laboratories in 1988 where she was named a Distinguished Member of the Technical Staff and later a Bell Labs Fellow. She served as head of the Scientific Computing Research Department from 1997-2000. In 2001 Wright became a professor of computer science and mathematics and chair of the Computer Science Department in the Courant Institute at New York University. Wright is a well known mathematician in the fields of optimization, linear algebra, numerical and scientific computing, and scientific and engineering applications. She has written two books on optimization with P.E. Gill and W. Murray, over 40 publications, and almost 50 technical reports for Stanford and Bell Laboratories. She has also served as associate editor for five journals. In 1995-1996, Wright served as President of the Society for Industrial and Applied Mathematics. She was elected to the National Academy of Engineering in 1997, to the American Academy of Arts and Sciences in 2001, and to the National Academy of Sciences in 2005. In 2000 she presented the AWM Noether Lecture. She received both the 2001 Award for Distinguished Service to the Profession from SIAM and the 2002 Award for Distinguished Public Service from the American Mathematical Society. The citation for the latter award noted that "Professor Wright has been active for many years in encouraging women and minority students, for example, by means of programs that brought them together with leaders and researchers from industry to discuss opportunities outside academia."

**Jianhong Wu**(York Institute for Health Research, York University)Jianhong Wu, Professor and Canada Research Chair in Applied Mathematics (Tier I), is a recipient of Alexander von Humboldt Fellowship, Cheung Kong Lecture Professorship, and Paul Erdos Visiting Professorship. He is the recipient of the 2003 Canadian Applied and Insudtrial Mzathematical Society Research Prize, and the 2002 Atlantic Association for Research in Mathematical Sciences Distinguished Lecturer. His research interests include Infinite Dimensional Dynamical Systems, Mathematical Biology, Neural Networks, Pattern Recognition and Clustering. He is serving in a number of editorial boards of international journals, co-edited 3 conference proceedings for the Fields Institute Communication Series and Canadian Applied Mathematics Quarterly, in addition to 2 co-edited special volumes on neural networks, 4 monographs and a number of journal publications. He is the Editor-in-Chief for Canadian Mathematical Bulletin (2006-2011), a member to the NSERC Grant Selection Committee (GSC337, 2001-04), a member to the College of Reviewers for Canada Research Chairs Program (2001-). He served the Board of Directors for MITACS (2004-05), the Board of Directors for CAIMS (2002-05), and the AARMS Scientific Review Panel (2002-05). He is chairing the CAIMS Research Prize Committee (2004-06), and is also serving at the CMS Research Committee (2003-05).

**Shing-Tung Yau**(Harvard University)Dr. Shing-Tung Yau, a Fields Medal recipient, serves as Professor of Mathematics at Harvard University. He also serves as Director of The Institute of Mathematical Sciences, at The Chinese University of Hong Kong. Dr. Yau’s fields of interest include differential equations and mathematical physics. He remains active at the interface between geometry and theoretical physics.

**Efim Zelmanov**(University of California, San Diego)Efim Zelmanov attended Novosibirsk State University, obtaining his Ph.D. in 1980 having had his research supervised by Shirshov and Bokut. His Ph.D. thesis completely changed the whole of the subject of Jordan algebras by extending results from the classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras. Zelmanov described this work on Jordan algebras in his invited lecture to the International Congress of Mathematicians at Warsaw in 1983. In 1980 Zelmanov was appointed as a Junior Researcher at the Institute of Mathematics of the Academy of Sciences of the USSR at Novosibirsk. By 1986 had had been promoted to Leading Researcher. In 1987 Zelmanov solved one of the big open questions in the theory of Lie algebras . He proved that the Engel identity ad(y)^n=0 implies that the algebra is necessarily nilpotent. This was a classical result for finite dimensional Lie algebras but Zelmanov proved that the result also held also for infinite dimensional Lie algebras. In 1990 Zelmanov was appointed a professor at the University of Wisconsin-Madison in the United States. He held this appointment until 1994 when he was appointed to the University of Chicago. In 1995 he spent the year at Yale University. In 1991, Zelmanov went on to settle one of the most fundamental results in the theory of groups: the restricted Burnside problem, which had occupied group theorists throughout the 20th century. In 1994 Zelmanov was awarded a Fields Medal for this work at the International Congress of Mathematicians in Zurich in 1994.

**James Zidek**(University of British Columbia)Jim Zidek is Professor in the Department of Statistics at the University of British Columbia. He received his Ph. D. in Stanford in 1967. His research ranges from his foundational work in decision theory and group Bayes analysis to his applied work in environmetrics. He is an Elected Fellow of Royal Society of Canada, Institute of Mathematical Statistics, the American Statistical Association and a member of International Statistical Institute. Zidek has received numerous awards, including the Ninth Eugene Lukacs Symposium Distinguished Service Award, the Statistical Society of Canada's Gold Medal, the Distinguished Achievement Medal of the Environmental Statistics Section of the ASA, and the Izaak Walton Killam Research Prize. He has served the statistical community in many ways, including as a member of numerous scholarly committees and editorial boards, and currently as Advisory Editor for CRC and Editor for Encyclopedia of Environmental Statistics. http://hajek.stat.ubc.ca/~jim/homepage.html