Title: Affine Grassmannians and Satake equivalence

         Description:

• . Contents:

1. Case of GL_n. Lusztig's relation to nilpotent orbits.
2. Modular and tannakian approach.
3. G(O)-orbits; G(O)-equivariant perverse sheaves.
4. Semiinfinite orbits; intersections of orbits.
5. Cohomology of G(O)-equivariant perverse sheaves.
6. Convolution; Fusion.
7. Fiber functor.
8. Tannakian formalism and Satake equivalence.
9. Toda lattice and G(O)xC^*-equivariant homology.
10. G(O)xC^*-equivariant derived category.
11. Asymptotic Harish-Chandra modules and Kostant-Whittaker reduction.

• Prerequisites:

the notions of semisimple Lie groups and Lie algebras, constructible sheaves, coherent sheaves, singular cohomology, preferably some homological algebra of derived categories.