New Topological Contexts for Galois Theory and Algebraic Geometry (08w5014)

Arriving in Banff, Alberta Sunday, March 9 and departing Friday March 14, 2008


(University of Glasgow)

(University of Hamburg)


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.