Justin Campbell, University of Chicago

Abstract: The geometric Satake equivalence identifies two apparently different symmetric monoidal abelian categories arising in geometric representation theory. It is a fundamental instance of geometric Langlands duality. This talk will be about some recent work with Sam Raskin in which we upgrade it to an equivalence of monoidal factorization categories, which in topological terms amount to E_3-monoidal infinity-categories. In particular, this leads to a stronger formulation of the Hecke compatibility in the global geometric Langlands correspondence.