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: