Goal:
The goal of this seminar is to learn about perverse sheaves and the geometric Satake equivalence. Instead of seminar talks, we will hold weekly meetings/discussions over assigned readings and complete exercises. We plan on keeping a shared, online journal amongst ourselves to highlight lingering questions and gather insights and thoughts that struck us during the readings. We also plan on keeping an online working document of partially/fully tex-ed up solutions.
Materials:
P. Achar, "Perverse sheaves and its applications in representation theory"
M. Goresky, lecture notes on perverse sheaves (here)
Supplementary materials and helpful notes will be gathered along the way and published onto this website.
Space-time coordinates:
Time: Fridays, 12-2pm
Venue: Math lounge
Schedule:
11/18: Chapter 1, sheaf theory (Marielle)
Summary: Ran through this chapter briefly, summarized the different functors and base-change theorems.
11/25: Chapter 1, sheaf theory (Together)
Summary: Completed some exercises from Chapter 1
12/2: Chapter 1, sheaf theory (Marielle)
Summary: Computations of push-forward of sheaves in Section 1.10
Break
01/13: Chapter 2, constructible sheaves (Emma)
Summary: orientation sheaf, basic definitions of stratification and constructibility.
01/20: Chapter 2.8, Verdier duality and proof (Marielle)
01/27: Chapter 2.11, Homology and Fundamental classes (Emma)
Summary: Boore-Moore homology
02/04: Chapter 3.1, Perverse sheaves (Marielle)
Summary: Appendix A.7 (generalities of t-structures), proving that the perverse t-structure is a t-structure
02/11: Computing examples of perverse sheaves (Yingdi)
Summary: For the inclusion j of a point into C, we computed j_! and j_* of the constant sheaf