Algebra and Geometry Seminar
Perverse sheaves have important applications in representation theory and number theory. In this talk we will consider the case of mod p étale sheaves on the affine Grassmannian over a field of characteristic p. Despite the pathological behavior of such sheaves, they encode the structure of mod p Hecke algebras. We will focus on a mod p version of the geometric Satake equivalence. Along the way we will encounter connections between Frobenius splittings and the general theory of perverse mod p étale sheaves.