Categorical Representation Theory and The Coarse Quotient

The main theorem of this talk will be that one can understand a “dense open” subset of categories with an action of GL_n in terms of the action of the symmetric group S_n acting on the complex vector space C^n, and a related statement for any other reductive group. We will start by introducing the notion of a categorical representation of a group and discuss some motivation. Then, we will discuss some of the main technical tools involved in making the statement of the main theorem precise. Time permitting, we will discuss how one can use these ideas to prove a “dense open” version of a conjecture of Ben-Zvi—Gunningham on the essential image of parabolic restriction.