Hecke algebras and motives (Robert Cass, CMC)

Hecke algebras play a central role in both number theory and representation theory. While some Hecke algebras have explicit descriptions in terms of generators and relations, others are understood through structure constants that encode multiplicities in tensor products of representations. In this talk, I will discuss several projects with Thibaud van den Hove and Jakob Scholbach aimed at using geometry and motives to give a uniform categorification of Hecke algebras. Along the way, we will encounter the geometric Satake equivalence, Gaitsgory’s central functor, and Iwahori-Whittaker models.