Iwahori-Whittaker category and geometric Casselman-Shalika

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 pp-adic groups, introduce the Iwahori-Whittaker model, and sketch the proof of the equivalence.