# The Geometric Satake Equivalence: MWF 2-2:50pm

Zoom link: https://bccte.zoom.us/j/91979071664

Lecture 1: Introduction via classical Satake isomorphism Video

Lecture 2: The functor-of-points approach to schemes Video

Lecture 3: Projectivity of the classical Grassmannian Video

Lecture 4: Ind-projectivity of the affine Grassmannian Video

Lecture 5: Loop groups Video

Lecture 6: The Schubert stratification of the affine Grassmannian Video

(Note: The definition of the stratification here is wrong and amounts to looking at the formal completion along each stratum. This is corrected in Lecture 7)

Lecture 7: Examples of open strata Video

Lecture 8: Smoothness of the strata in general Video

Lecture 9: Closure relations and the Satake category Video

Lecture 10: A haphazard introduction to perverse sheaves Video

Lecture 11: Towards the semisimplicity of the Satake category Video

Lecture 12: Semisimplicity of the Satake category Video

Lecture 13: Wrapping up semisimplicity Video

Lecture 14: Convolution in the Satake category Video

Lecture 15: Exactness of convolution I Video

Lecture 16: Exactness of convolution II Video

Lecture 17: The Beilinson-Drinfeld affine Grassmannian Video

Lecture 18: The commutativity constraint using fusion Video

Lecture 19: Musing on the monoidal structure on the cohomology functor Video

Lecture 20: The monoidal structure on the cohomology functor Video

Lecture 21: The Bruhat-Tits building and semi-infinite orbits for GL_2 Video

Lecture 22: Properties of semi-infinite orbits I Video

## References

1. Baumann and Riche, "Notes on the geometric Satake equivalence", https://arxiv.org/abs/1703.07288

2. T. Richarz, 'Basics on affine Grassmannians', https://timo-richarz.com/wp-content/uploads/2020/02/BoAG_02.pdf

3. Xinwen Zhu, "An introduction to affine Grassmannians and the geometric Satake equivalence", https://arxiv.org/abs/1603.05593