Speaker
Thibaud van den Hove
Description
The spherical and Iwahori-Hecke algebras of a reductive group are of great importance in the Langlands program. They are categorified by equivariant sheaves on the affine Grassmannian and affine flag variety respectively. Similarly, the Satake and Bernstein isomorphisms are categorified by the geometric Satake equivalence and Gaitsgory's central functor, for which one needs a choice of cohomology theory. In this talk, I will explain how to construct motivic refinements of these functors, so that the choice of cohomology theory is irrelevant. In particular, this yields "mixed" versions of both constructions. This is joint work with Robert Cass and Jakob Scholbach.