Speaker: Thomas Gannon (University of Texas)

Title: Categorical Representation Theory and the Coarse Quotient

Abstract: The main theorem of this talk will be that one can understand a "dense open" subset of DG categories with an action of a split reductive group G over a field of characteristic zero entirely in terms of its root datum. We will start by introducing the notion of a categorical representation of G and discuss some motivation. Then, we will discuss some of the main technical tools involved in making the statement of the main theorem precise, including discussion of the "coarse quotient" of the dual maximal Cartan by the affine Weyl group. We will also discuss how sheaves on this coarse quotient can be identified with bi-Whittaker sheaves on G, obtaining symmetric monoidal upgrade of a result of Ginzburg and Lonergan, and then give an outline of the proof of the main theorem. Time permitting, we will discuss some applications of these categorical representation theoretic ideas which prove a modified version of a conjecture of Ben-Zvi and Gunningham on the essential image of parabolic restriction.