Postdoctoral Math Seminar

The geometric Satake equivalence, due to Ginzburg and Mirkovic-Vilonen, identifies spherical perverse sheaves on the affine Grassmannian with representations of the Langlands dual group. It is an equivalence of symmetric monoidal abelian categories, which is compatible in some sense with the factorization structure of the affine Grassmannian. The equivalence does not hold at the level of derived categories, and Bezrukavnikov-Finkelberg showed how to enhance the spectral side to obtain a derived geometric Satake equivalence, although their methods are not compatible with factorization. I will explain how to make sense of the spectral Hecke category factorizably, which allows us to reprove the derived geometric Satake equivalence independently of Bezrukavnikov-Finkelberg's work, and to formulate an enhanced Hecke compatibility for the global geometric Langlands equivalence.