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...
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...
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
$D(G)$...
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...
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...
Before the "geometric Satake equivalence" there was a
decategorified version of it which however contained most of its
essential features. In my talk I will talk about some of the ideas
which have led to this theory. In particular I will explain
the...
Broue's Conjecture for $SL_2(\mathbb{F}_q)$ in defining
characteristic, predicts a derived equivalence between the
principal block of this group and the principal block of a Borel. A
structurally similar equivalence exist in the case of the...
