SCIENTIFIC PROGRAMS AND ACTIVITIES
|July 13, 2020|
OverviewEmerging from foundational work by Borel, Chevalley, Demazure, Grothendieck, Serre and Tits, the theory of group schemes has become an important part of the modern mathematical culture. Inspired by the theory of Lie algebras and groups on the one hand and classical algebraic geometry on the other, group schemes have developed into an important tool for understanding representation theory, linear algebraic groups, homogeneous spaces and torsors. Several deep open conjectures in modern algebraic geometry, number theory and representation theory (e.g., Serre's conjectures and the Langland's program) are formulated using the language of group schemes.
One example of important work in the theory of group schemes is the celebrated Grothendieck--Serre conjecture of the 1960's, which stated that any rationally trivial G-torsor, where G is a reductive group scheme over a regular local ring, is locally trivial in the Zariski topology. The study of this problem has a long history, with contributions made by many famous mathematicians (beginning with Serre himself). The problem has only recently been solved by Fedorov and Panin in 2012-2014. Another striking example is the theory of motives and the proof of the Milnor conjecture by Voevodsky, which was essentially based on the computations of the motives of certain homogeneous varieties under the action of the orthogonal group scheme.
This workshop will bring together leading experts and junior mathematicians working in this exciting field. It will include expository lectures aimed at graduate students and postdoctoral fellows, as well as research talks. There is financial support available for junior participants. Those interested should submit their request online.
The workshop activities will take place at 585 King Edward Avenue, Room B005 (on the University of Ottawa campus).