Hochschild cohomology of flag varieties and Kostant's tensor square conjecture

Tuesday, 9-July-2024 

Abstract

Flag varieties occupy a distinguished position in geometry, representation theory, and algebraic combinatorics and offer a rich source of interplay between these three subjects. At its inception in the mid-twentieth century, the goal of geometric representation theory was to understand the interaction between algebraic objects and their representations and geometric or topological invariants of flag (and related) varieties. In this talk, we will use this classical machinery to relate a relatively-unknown geometric invariant of the flag variety—its Hochschild cohomology—to a representation-theoretic problem known as Kostant's tensor square conjecture.