Abstract: We prove an equivalence between the equivariant derived category of constructible sheaves on the loop space of n-by-n matrices and the category of perfect complexes on a certain formal dg algebra. This equivalence is compatible with actions of the derived Satake category. I will explain how our result is related to conjectural dualities in the Langlands program and in physics. The proof involves certain invariant theoretic properties of a certain "dual" cotangent bundle. This is joint work with Tsao-Hsien Chen (in preparation).
Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.