Abstract: As a first step toward Bezrukavnikov's equivalence we will describe the geometric Satake equivalence, which categorifies the classical Satake isomorphism for the unramified Hecke algebra. It is also a cornerstone of the geometric Langlands program and plays a fundamental role in geometric constructions of Langlands correspondences, such as in the works of V. Lafforgue and Fargues-Scholze. Along the way we will discuss equivariant perverse sheaves, the affine Grassmannian, and the representation theory of reductive algebraic groups.

Seminar webpage: https://umrep.github.io/