SCIENTIFIC PROGRAMS AND ACTIVITIES

April 24, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Organizers: Vladimir Chernousov (Alberta) and Kirill Zainoulline (Ottawa)

Registration open,
on line to May 24

Students and PDF application for travel support now closed
Deadline to apply was March 15.
Accommodation Resources Getting to UOttawa
OVERVIEW

In the last 10-15 years the theory of linear algebraic groups has witnessed an intrusion of the cohomological methods of modern algebraic geometry and algebraic topology. These new methods have led to breakthroughs on a number of classical problems in algebra, which are beyond the reach of earlier purely algebraic techniques. The workshop will focus at the following new emerging techniques and applications:

- The proof of the Grothendieck-Serre conjecture based on the theory of affine Grassmannians.
The Grothendieck-Serre conjecture stated in 60's says that any rationally trivial G-bundle is locally trivial (in Zariski topology), where G is a smooth reductive group scheme over a local regular ring. In a recent preprint (Nov. 2012) Fedorov and Panin proved the conjecture in the geometric case using new connections with the theory of affine Grassmannians.

- Computation of generalized equivariant cohomology of projective homogeneous and toric varieties.
The notion of an algebraic oriented cohomology theory was introduced and extensively studied during the last decade by Levine, Morel, Panin, Smirnov and others. The universal such theory called algebraic cobordism has many applications in the theory of quadratic forms and homogeneous spaces. Its equivariant version is believed to contain all the information concerning cohomological behaviour of homogeneous spaces. In particular, its computation can lead to a better understanding of cohomology and related combinatorics of toric varieties.

OUTLINE OF THE PROGRAM

The workshop will run for three full days and a morning session during the fourth day (Friday morning - Monday noon) and will feature a unique combination of two introductory mini-courses and research-level talks. The two mini-courses will have three 80 min. lectures each and directed towards PhD students and young researchers. The topics are the following.
(a) Toric varieties and equivariant cohomology by Kalle Karu, University of British Columbia
- The course will be an introduction to toric varieties and equivariant cohomology.

(b) Introduction to principal homogeneous spaces by Roman Fedorov, Kansas State University
- The course will be devoted to the basics in the theory of torsors and the Grothendieck-Serre conjecture.

Besides the two mini-courses, there will be invited one-hour talks by the leading experts in the area, as well as short talks by young researchers, postdocs and graduate students.

INVITED SPEAKERS confirmed as of January 3, 2014

Alex Duncan, University of Michigan
Stefan Gille, University of Alberta
Nikita Karpenko, University of Alberta
Daniel Krashen, University of Georgia
Nicole Lemire, Western University
Alexander Merkurjev, University of California at Los-Angeles
Julia Pevtsova, University of Washington
Andrei Rapinchuk, University of Virginia
Zinovy Reichstein, University of British Columbia

FINANCIAL SUPPORT

Some funding is available for graduate students and postdoctoral fellows. Please, apply via the web-site of the workshop.

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Participants may also be interested in a closely related event, the 73rd Algebra Day on April 27, 2014, also at the University of Ottawa.

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