Lecture Series

Koszul duality and characters of tilting modules

Geordie Williamson (University of Sydney and Bonn Research Fellow/HCM)


Date, Time, and Location:

Wednesday, June 19, 2019
Lecture I
12 pm - 1 pm, Lipschitzsaal, Mathezentrum, Endenicher Allee 60, Bonn

Wednesday, June 26, 2019
Lecture II
12 pm - 1 pm, Lipschitzsaal, Mathezentrum, Endenicher Allee 60, Bonn

Wednesday, July 3, 2019
Lecture III
11 am - 12 pm, Lipschitzsaal, Mathezentrum, Endenicher Allee 60, Bonn

 

Abstract

Recently Achar, Makisumi, Riche and I have completed a program to determine the characters of tilting modules for algebraic groups in terms of the p-canonical basis of Hecke algebras. Subsequently, Riche and I explained how this leads to a rather simple reformulation of Lusztig’s character formula. I will try to explain the main ideas; the most important being modular versions of equivalences categorifying the Deligne-Langlands conjecture, and a form of Koszul duality. I will assume some background in reductive algebraic groups and their representation theory, as well as some familiarity with the Hecke category. The lectures will be loosely based on the three papers:

https://arxiv.org/abs/1703.05843,

https://arxiv.org/abs/1706.00183,

https://arxiv.org/abs/1904.08085


The three lectures are specifically addressed to local postdocs, PhD students, and master students. No registration needed.