Geometric and Modular Representation Theory Seminar

This talk will be an exposition of a recent paper of Bezrukavnikov-Gaitsgory-Mirkovic-Riche-Rider giving an Iwahori-Whittaker model for the Satake category. The main point is that their argument works for modular coefficients. I will give some motivation via the Casselman-Shalika formula in the theory of $p$-adic groups, introduce the Iwahori-Whittaker model, and sketch the proof of the equivalence.