The affine Grassmannian and geometric Satake

From lattice counts and spherical Hecke algebras to geometric and derived Satake: loop groups, Schubert varieties, weight functors, convolution, fusion and the Langlands dual group.

1. Spherical Hecke algebras as functions on the affine Grassmannian
2. Loop groups and the affine Grassmannian
3. Beauville–Laszlo gluing and the moduli interpretation
4. Orbits and Schubert varieties in the affine Grassmannian
5. Semi-infinite orbits and weight functors
6. The Satake category
7. Convolution and rigidity
8. Fusion and the commutativity constraint
9. Tannakian categories
10. The fibre functor and the Tannakian group
11. The Mirković–Vilonen theorem: identifying the dual group
12. Consequences and examples
13. Derived Satake

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