08w5014 New Topological Contexts for Galois Theory and Algebraic Geometry

Arriving Sunday, March 9 and departing Friday, March 14, 2008

Organizers: Andrew Baker (University of Glasgow/University of Oslo), Birgit Richter (University of Hamburg).

Confirmed Participants

Press Release: New Topological Contexts for Galois Theory and Algebraic Geometry

Information for Participants

Proceedings (external link)

Steffen Sagave's talk
DG-algebras and derived A-infinity algebras (external link, pdf)

Paul Goerss' talk
Realizing Families of Landweber Exact Theories (external link, pdf)

Maria Basterra's talk
Topological Andre-Quillen Cohomology and Related Topics (external link, pdf)

Christian Schlichtkrull's talk
Algebraic K-theory and traces for structured ring spectra (external link, pdf)

Schedule and Abstracts (PDF file)

Final Report (PDF file)

Workshop Videos

Objectives

Following the foundational developments during the last decade, the subject area seems to be moving into a period in which applications can be seen. On the other hand the further investigation of the theoretical aspects is inevitably becoming more difficult. It is therefore important that researchers in this subject area are aware of the accumulated knowledge of the past as well as gaining a perspective on future directions. In particular we hope that the workshop will initiate interactions with algebraists and algebraic geometers. A specialist meeting of this type in the near future thus appears extremely desirable.

We aim to bring together a wide ranging group of mathematicians including a mixture of emph{internationally leading experts} on the relevant parts of algebraic topology, emph{internationally leading experts} on topics related to the subject matter, and emph{younger topologists} (late in doctoral training or beginning postdoctoral activity) who will benefit from exposure to state of the art talks and other interaction with the above groups. Especially in regard to the latter, we will ensure that the talks included a kernel of high quality expository or overview talks aimed at introducing people to the subject area and encouraging future research activity, especially by people not currently actively working on it.

The size of the workshop with at most 40 participants seems likely to enhance the chances of interactions between small groups of individuals and we expect that significant collaborative research will be carried out at the workshop or as a direct result of it. We also envisage that a written outcome of the workshop would result, including versions of some of the main talks as well as and well-prepared introductory or survey talks. The organizers have had previous experience of this with a similarly sized meeting held in Glasgow in 2002 that led to a book containing such articles achieving these goals, and which was followed by several other meetings on related subject areas.

The formal structure of the meeting would include a series of major invited talks or short series of talks surveying aspects of the subject area and related mathematics, more specialized talks on current research by individual participants selected from titles offered after acceptance of invitations to attend, and talks by early-career participants together with informal discussion sessions and problem sessions. We feel that it is particularly important not to overload the formal programme so as to which would reduce the time for less structured but often very productive interactions between individuals. Thus we propose that there be a maximum of 5 hours of talks per day, with adequate breaks between to allow for discussion and audience reaction.

Amongst the proposed participants we have included people working within algebraic topology as well as some specialists in other areas which have close connections with the subject matter, such as Hopf-Galois extensions, motivic homotopy theory and algebraic K-theory. We expect these would provide useful cross-disciplinary input especially through survey talks.