Winter 2026
- Week 2 (January 12): Justin Bloom
- Title: Actions on cohomology
- Abstract: There are very important representations of reductive groups which occur as cohomology of some line bundle over a G-variety.
We'll review the geometry of sheaves in order to see how to generalize these kinds of representations, and what can go wrong.
- Week 3 (January 19): MLK ☮ Day
- "The student movements have done more to save the soul of the nation than anything I can think of"
- Week 4 (January 26): Justin Bloom
- Title: Character theory
- Abstract: We'll define `generalized characters' for a Lie group or a group scheme and look at applications.
We'll look at classical characters and Brauer characters for finite groups, and some character theory for reductive groups.
- Week 5 (February 2): Andrew Aguilar
- Title: How to Support Representation Theorists
- Abstract: have you wondered how support theory is used in representation theory?
Support varieties for modules over a finite group were first defined by Carlson in the 1980s and was fully utilized in the 1990s by
Benson, Carlson and Rickard to classify the thick tensor ideals in the stable category.
Then in 2005 Balmer’s seminal paper put this classification into the broader context of Tensor Triangular Geometry.
After which, the progress has not stopped; now aiming towards a similar classification for big categories.
In this talk we’ll discuss the necessary background needed to understand the current work and how support plays a role.
- Week 6 (February 9): Wolfgang Allred
- Title: Equivariant sheaves through examples
- Abstract: We will continue the theme from last time and will study equivariant sheaves from the perspective of representation theory.
We will begin with some definitions and then spend the rest of the talk working through some examples.
- Week 7 (February 16):
President's day
- Week 8 (February 23): Ting Gong
- Week 9 (March 2): TBA
- Week 10 (March 9): TBA