Algebraic Geometry Seminar: Clemens Koppensteiner

In this talk I will discuss how to compute the Hochschild cohomology of the category of D-modules on a quotient stack via a compactification of the diagonal morphism. I will then apply this construction to the case of quotients by a torus and describe the Hochschild cohomology as the cohomology of a D-module on the loop space of the quotient stack. This work is motivated by a desire to understand the D-module equivalent of singular support of coherent sheaves in Geometric Langlands.