The Affine Grassmannian is an ind-scheme associated to a reductive
group G. It has a cell structure similar to the one in the usual
Grassmannian. Transversal slices to these cells give an interesting
family of Poisson varieties. Some of them admit a smooth symplectic
resolution and have an interesting geometry related to the
representation theory of the Langlands dual group. We will focus on
equivariant cohomology of such resolutions and will show how the
trigonometric Knizhnik-Zamolodchikov equation arises as a quantum
differential equation in this setting.