Derived Equivariant Cohomology of the affine Grassmannian and Bezrukavnikov and Finkelberg’s equivalences

This is the third talk in a series of three talks on the derived Satake equivalence. I will give an overview of the article of Bezrukavnikov and Finkelberg which explains how the equivariant derived category of the affine Grassmannian can be described in terms of coherent sheaves on the Langlands dual Lie algebra.