Previous Special Year Seminar

Feb
02
2021

SL2 Seminar

User's guide to computing with tilting modules
Benjamin Elias
3:00pm|Remote Access

A basic technique in algebra, when describing a difficult-to-approach category like Tilt, is to choose a projective generator and study its endomorphism ring. The modern twist on this technique is to choose the projective generator with great...

Jan
28
2021

Quantum Groups Seminar

Introduction to quantized enveloping algebras
Leonardo Maltoni
4:00pm|Remote Access

Continuation of the talk from last time.

Jan
27
2021

Geometric and Modular Representation Theory Seminar

The Hecke category action on the principal block via Smith theory
Geordie Williamson
3:00pm|Simonyi Hall 101 and Remote Access

Wall-crossing functors on the principal block of category $O$ give an action of the (finite) Hecke category. If one knows enough about the Hecke category, one can deduce the Kazhdan-Lusztig conjectures from the existence of this action. This is a...

Jan
26
2021

SL2 Seminar

Why do we care about characters of tilting modules?
Shotaro Makisumi
3:00pm|Remote Access

I will explain the basics of tilting modules for reductive algebraic groups and why we should care about their characters. In particular, I will discuss Donkin's tensor product theorem and the relation to modular representations of symmetric groups...

Jan
21
2021

Quantum Groups Seminar

Introduction to quantized enveloping algebras
Leonardo Maltoni
4:00pm|Remote Access

This talk covers Chapters 4 and 5 in Jantzen's book.

Jan
20
2021

Geometric and Modular Representation Theory Seminar

The linkage principle and the tilting character formula via Smith-Treumann theory
Daniel Juteau
3:00pm|Simonyi Hall 101 and Remote Access

The linkage principle says that the category of representations of a reductive group $G$ in positive characteristic decomposes into "blocks" controlled by the affine Weyl group. We will discuss the beautiful geometric proof of this result that Simon...

Jan
19
2021

SL2 Seminar

A categorical approach to representations in defining characteristic
Nate Harman
3:00pm|Remote Access

Let $G$ be an algebraic group defined over a finite field $F_q$. Through the lens of Tannakian formalism I will give a categorical description of the relationship between the representation theory of the algebraic group $G$ and the representation...

Jan
13
2021

Geometric and Modular Representation Theory Seminar

Introduction to Smith theory
Tony Feng
3:00pm|Simonyi Hall 101 and Remote Access

Smith theory is a type of equivariant localization with respect to a cyclic group of prime order $p$, with coefficients in a field of the same characteristic $p$. It has been the source of various recent advances in modular representation theory and...

Dec
16
2020

Geometric and Modular Representation Theory Seminar

Hecke category via derived convolution formalism
Dima Arinkin
3:00pm|Remote Access

The talk is about convolution in the setting of geometric representation theory. What are its formal properties? As a starting point, let $G$ be a group and let $D(G)$ be the derived category of constructible sheaves on it. Convolution turns $D(G)$...