Geometric and categorical representation theory

Abstracts

8. The loop space and representations - 1

Roman Bezrukavnikov

10/23/23, 9:00 AM

I will talk about (relatively) recent ways to apply the affine Grassmannian as an algebro-geometric or topological object to representation theory of the reductive group in positive characteristic or quantum group at a root of unity.
Based on works (mostly in progress) with Boixeda Alvarez, McBreen, Yun, Shan, Vasserot
and Arinkin.

6. Representations of p-adic groups - 1

Jessica Fintzen

10/23/23, 11:00 AM

The mini course will provide an introduction to the representation theory of p-adic groups via type theory. The course will include:
- basic definitions surrounding representations of p-adic groups
- an introduction to Bruhat-Tits theory and Moy-Prasad filtrations
- construction of supercuspidal representations: depth-zero representations, (a glimpse of) Yu's construction
- Bernstein...

2. Braid group action on the cohomology of Deligne-Lusztig varieties

Cédric Bonnafé

10/23/23, 4:00 PM

If B is the braid group associated with the Weyl group W of a split reductive group G over F_q, and if b is in B, we construct a categorical action of the centralizer C_B(b) on the cohomology of the Deligne-Lusztig variety X(b) associated with b. If b=1, we retrieve the classical algebraic action of the Hecke algebra on the permutation representation of the finite flag variety. As another...

4. The integral motivic Satake equivalence

Robert Cass

10/23/23, 5:30 PM

The geometric Satake equivalence describes the representation theory of the Langlands dual of a split reductive group in terms of sheaves on the affine Grassmannian. Numerous versions of this equivalence are known for different base schemes and cohomology theories, each having their own applications in geometric representation theory. In this talk we discuss a Satake equivalence for integral...

13. Dg trace and center of Hecke categories - 1

Matt Hogancamp

10/24/23, 9:00 AM

In this minicourse we will consider the categorification of some quintessential constructions in linear algebra and representation theory, particularly the notion of (co)center of an algebra, and applications to Hecke categories.

Talk 1 will introduce a dg version of the usual Drinfeld center and "horizontal trace" of a monoidal category.

Talk 2 will discuss dg analogues of highest...

11. The loop space and representations - 2

Roman Bezrukavnikov

10/24/23, 11:00 AM

I will talk about (relatively) recent ways to apply the affine Grassmannian as an algebro-geometric or topological object to representation theory of the reductive group in positive characteristic or quantum group at a root of unity.
Based on works (mostly in progress) with Boixeda Alvarez, McBreen, Yun, Shan, Vasserot
and Arinkin.

9. Representations of p-adic groups - 2

Jessica Fintzen

10/25/23, 9:00 AM

The mini course will provide an introduction to the representation theory of p-adic groups via type theory. The course will include:
- basic definitions surrounding representations of p-adic groups
- an introduction to Bruhat-Tits theory and Moy-Prasad filtrations
- construction of supercuspidal representations: depth-zero representations, (a glimpse of) Yu's construction
- Bernstein...

14. Dg trace and center of Hecke categories - 2

Matt Hogancamp

10/25/23, 11:00 AM

In this minicourse we will consider the categorification of some quintessential constructions in linear algebra and representation theory, particularly the notion of (co)center of an algebra, and applications to Hecke categories.

Talk 1 will introduce a dg version of the usual Drinfeld center and "horizontal trace" of a monoidal category.

Talk 2 will discuss dg analogues of highest...

7. A Fourier transform for unipotent representations of p-adic groups

Beth Romano

10/25/23, 4:00 PM

In the representation theory of finite reductive groups, an essential role is played by Lusztig's nonabelian Fourier transform, an involution on the space of unipotent characters of the group. For reductive p-adic groups, the unipotent local Langlands correspondence gives a natural parametrization of irreducible smooth representations with unipotent cuspidal support. However, many questions...

16. Some finiteness properties of Hecke rings of p-adic groups

Jean-François Dat

10/25/23, 5:30 PM

If K is a compact open subgroup of a p-adic group G, the fact that any double K-coset in G is the union of finitely many left K-cosets allows one to define the Hecke ring Z[K\G/K] of the pair (G,K). When K is a hyperspecial subgroup, the C-algebra C[K\G/K] is a f.g. commutative algebra that was described by Satake, and this was the starting point of the Langlands program for automorphic...

12. The loop space and representations - 3

Roman Bezrukavnikov

10/26/23, 9:00 AM

I will talk about (relatively) recent ways to apply the affine Grassmannian as an algebro-geometric or topological object to representation theory of the reductive group in positive characteristic or quantum group at a root of unity.
Based on works (mostly in progress) with Boixeda Alvarez, McBreen, Yun, Shan, Vasserot
and Arinkin.

10. Representations of p-adic groups - 3

Jessica Fintzen

10/26/23, 11:00 AM

The mini course will provide an introduction to the representation theory of p-adic groups via type theory. The course will include:
- basic definitions surrounding representations of p-adic groups
- an introduction to Bruhat-Tits theory and Moy-Prasad filtrations
- construction of supercuspidal representations: depth-zero representations, (a glimpse of) Yu's construction
- Bernstein...

1. Arkhipov-Bezrukavnikov for p-adic groups

João Lourenço

10/26/23, 4:00 PM

We are going to explain joint work with Johannes Anschütz, Zhiyou Wu, and Jize Yu concerning the Arkhipov--Bezrukavnikov equivalence in mixed characteristic. Kazhdan--Lusztig constructed an isomorphism between the Grothendieck group of equivariant coherent sheaves on the dual Springer variety, and that of equivariant perverse sheaves on the Iwahori flag variety in the function field case....

5. Quantum category O vs affine Hecke category

Ivan Loseu

10/26/23, 5:30 PM

I will establish an equivalence between a block of the quantum category O at an odd root of unity and the heart of the "new" t-structure on a suitably singular affine Hecke category

15. Dg trace and center of Hecke categories - 3

Matt Hogancamp

10/27/23, 8:50 AM

In this minicourse we will consider the categorification of some quintessential constructions in linear algebra and representation theory, particularly the notion of (co)center of an algebra, and applications to Hecke categories.

Talk 1 will introduce a dg version of the usual Drinfeld center and "horizontal trace" of a monoidal category.

Talk 2 will discuss dg analogues of highest...

3. The anti-spherical Hecke category for Hermitian symmetric pairs

Maud De Visscher

10/27/23, 10:20 AM

In this talk, I will discuss the representation theory of the anti-spherical Hecke categories for Hermitian symmetric pairs (W,P) over a field k of characteristic p. Minimal coset representatives for Hermitian symmetric pairs are fully commutative elements (as defined by Stembridge) and we will see how this property implies a much simplified diagrammatic presentation for the corresponding...