For any complex reductive group G one can associate a geometric object called the Affine Grassmannian. The transversal slices are interesting affine Poisson varieties appearing in this geometry. In this talk I’ll focus on the equivariant quantum cohomology of these spaces. In particular, I’ll show how the quantum differential equation in types ADE can be identified with the trigonometric Knizhnik-Zamolodchikov equation.