Coherent Satake Functor

To a reductive group G one can associate the so-called Langlands dual group G^. The category of representations of G^ can be recovered as the category of certain D-modules on the so-called affine Grassmannain. (In fact, this can be taken as the definition of G^ via the Tannakian formalism).
 
I will discuss this equivalence of categories, known as the geometric Satake equivalence, in details. This equivalence is a part of the local Langlands duality. The aim of D. Arinkin and the speaker is to construct the quasi-classical limit of the Satake equivalence, laying foundations for the local Hitchin-Langlands duality.
 
No previous knowledge of D-modules, affine Grassmannians, or the Langlands program will be assumed.