Hecke category via derived convolution formalism

The talk is about convolution in the setting of geometric representation theory. What are its formal properties? As a starting point, let G be a group and let D(G) be the derived category of constructible sheaves on it. Convolution turns D(G) into a monoidal category, which is rigid (every object is dualizable) if and only if G is proper (this statement is due to Boyarchenko and Drinfeld).

 

In this talk, I develop the formalism of convolution using the language of derived algebraic geometry, and then apply these techniques to the (spherical) Hecke category and related objects.

Date

Affiliation

University of Wisconsin–Madison

Speakers

Dima Arinkin