Previous Special Year Seminar

Mar
18
2021

Quantum Groups Seminar

Algebraic groups and all in characteristic p
Ivan Loseu
4:00pm|Remote Access

The talk discusses basics of quantum groups at roots of unity with motivation from modular representation theory.

Mar
17
2021

Geometric and Modular Representation Theory Seminar

Affine Hecke category and noncommutative Springer resolution
Roman Bezrukavnikov
3:00pm|Simonyi Hall 101 and Remote Access

I will start with a few comments on the proof of the equivalence presented in the previous talks. Then I will focus on the description of the abelian category of perverse sheaves on the affine flag variety on the coherent side, where the answer is...

Mar
16
2021

SL2 Seminar

Microlocal sheaves II: morphisms, microperverse sheaves and regular singularities
Michael McBreen
6:00pm|Remote Access

We introduce basic tools of the trade: the Fourier-Sato transform, specialisation, Sato's microlocalisation and the microhom functor, culminating with a concrete description of the morphisms in our category of microlocal sheaves. We use quantized...

Mar
10
2021

Geometric and Modular Representation Theory Seminar

Two Geometric Realizations of the Affine Hecke Algebra I
Pablo Boixeda Alvarez
3:00pm|Simonyi Hall 101 and Remote Access

In this talk we will begin the discussion of the results in Bezrukavnikov's "On Two Geometric Realizations of the Affine Hecke algebra". We will put all the previous tools described in this series of talks together to construct the equivalence of...

Mar
09
2021

SL2 Seminar

A friendly introduction to microlocal sheaves
Michael McBreen
5:00pm|Remote Access

We will study the singularities of sheaves on a manifold via the symplectic geometry of its cotangent bundle, following the work of Sato, Kashiwara, Schapira and others. We will then see how to organise this information into a sheaf of categories...

Mar
04
2021

Quantum Groups Seminar

Braid group actions and PBW type basis
Calder Morton-Ferguson
4:00pm|Remote Access

Covers chapter 8 in Jantzen's book.

Mar
03
2021

Geometric and Modular Representation Theory Seminar

On two geometric realizations of the anti-spherical module
Tsao-Hsien Chen
3:00pm|Simonyi Hall 101 and Remote Access

The anti-spherical modules over the affine Hecke algebras admit two different realizations: one realization is in terms of the space of Whittaker functions on the affine flag manifolds and the other realization, due to Kazhdan-Lusztig, is in terms...

Feb
25
2021

Quantum Groups Seminar

R-matrices
Elijah Bodish
4:00pm|Remote Access

Continuation of the talk from last time.