# Satake Equivalence

Organizers: Runlei Xiao, Khai-Hoan Nguyen-Dang

Time: The seminar will be held on Friday, room (TBA), from 14:00. The first talk will take place on November 24

Goal: The first part of the seminar will focus on the affine Grassmannians.

The second part of the seminar will introduce the geometric Satake equivalence.

We mainly follow the lecture notes by Xinwen Zhu.

An outline for the seminar can be found here.

Tentative Schedule

Talk I: [Zhu16][1.1] - November 24, room 2AB40, 13:30-14:30

• Introduce the functor point of view

Introduce the usual Grassmannians, and prove that they are projective schemes

Briefly disscuss about the affine Grassmannians.

Speaker: Runlei Xiao

Talk II: [Zhu16][1.2, 1.3] December 1, room 2AB40, 14:00-15:00

• Introduce the affine Grassmannians of GL_n

Explain the notion of ind-scheme, and the theorem states that the affine Grassmannian of GL_n is represented by an ind-projective scheme.

• Introduce the affine Grassmannians of general groups and their properties.

Speaker: Khai-Hoan Nguyen-Dang

Talk III: [Zhu16][1.5, 1.6, 1.7] December 15, room 430 (4DA2), 13:00-14:00

• Introduce jet and loop groups and their properties.

• Discuss the moduli interpretation of Grassmannian due to Beauville-Laszlo.

If time permits

• Examine the affine Grassmannians over complex numbers.

• Examine the affine Grassmannian over p-adic fields.

Speaker: Runlei Xiao

Talk IV: [Zhu16][2.1] January 26, room 1BC50, 13:30-14:30

•Introduce Schubert varieties and Schubert cells in the classical case (partial flag variety), and then for affine Grassmannians.

Speaker: Khai-Hoan Nguyen-Dang

Talk V: [Zhu16][3.1, 3.2] February 09, room 1BC50, 14:00-15:00

• Beilinson-Drinfeld Grassmannians

• Factorization theorem

Speaker: Khai-Hoan Nguyen-Dang

Talk VI: [Zhu16][Appendix A.1 , 5.1]

• Perverse Sheaf

• Satake catgory

Speaker: Runlei Xiao

Talk VII: [Zhu16][5.2]

• Tannakian category

• Satake as Tannakian category

Speaker: Khai-Hoan Nguyen-Dang

Talk VIII: [Zhu16][5.3, 5.4]

• Langlands dual group

• Fusion product

Speaker: Runlei Xiao

Talk IX: [Zhu16][5.5, 5.6]

• Geometric Satake Isomorphism

• Relation with classical Satake isomorphism

Speaker: