Previous Special Year Seminar

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 $D(G)$...

Dec
15
2020

SL2 Seminar

Cohomology: qualitative and stable results
Eric M. Friedlander
3:00pm|Remote Access

We survey work over the last 50 years advancing our understandingof cohomology of groups. We begin with results of Daniel Quillen which have influenced all that follows. We mention stability results of Cline, Parshall, Scott, and van der Kallen...

Dec
09
2020

Geometric and Modular Representation Theory Seminar

Lefschetz operators, Hodge-Riemann forms, and representations
Peter Fiebig
3:00pm|Simonyi Hall 101 and Remote Access

Motivated by a formal similarity between the Hard Lefschetz theorem and the geometric Satake equivalence we study vector spaces that are graded by a weight lattice and are endowed with linear operators in simple root directions. We allow field...