Linear Algebraic Groups and Related Structures (09w5026)


Vladimir Chernousov (University of Alberta)

(University of California at Los Angeles)

(Western University)

Zinovy Reichstein (University of British Columbia)


The Banff International Research Station will host the "Linear Algebraic Groups and Related Structures" workshop next week, September 13 - September 18, 2009.

At the turn of the 20th century, the great German mathematician Felix Klein championed the idea that geometric fugures can be best understood by studying their symmetries. These symmetries form a structure called a group. In the past
100 years Klein's idea has proved to be extremely fruitful in geometry as well as in many other parts of mathematics, theoretical physics and chemistry.

This workshop aims to explore the Klein's vision in the algebraic context. The symmetries of various algebraic objects (e.g., quadratic forms, finite-dimensional algebras or algebraic varieties) form important and intrinsically beautiful structures called algebraic groups. The theory of algebraic groups was founded by A. Borel, C. Chevalley, M. Demazure, A. Grothendieck, T. A. Springer and J.-P. Serre in the 1950s and 60s. In recent years there has been
rapid progress in this subject. Several important long-standing open problems have been either completely or partially solved. In 2002 a Fields medal for ground-breaking work in this area was awarded to V. Voevodsky; in subsequent
years the subject continued to develop at a rapid pace.

The workshop is intended to provide a forum for the experts to discuss their latest work and for younger researchers to learn about open problems and state of the art techniques in this exciting and rapidly developing field.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).