Prof. Peter Fiebig (University of Erlangen) – Geometric Methods in Representation Theory Seminar

Title: Sheaves on the alcoves and modular representations

Abstract: The main topic is the problem of determining the characters of reductive algebraic groups over a field of positive characteristic. Since Williamson gave countless (unexpected) examples of characters that differ from the character formula given by George Lusztig in 1980 (which holds for large enough characteristics), the community is hoping for a revised formula, or an effective algorithm, that provides a solution in the general case. For this, one surely needs a much better understanding on the torsion phenomena occurring for small primes. In my talk I first want to give an understandable introduction to the problem, and then I want to introduce a new category related to modular representation theory that hopefully will help us understand the problem in greater depth.