Seminars Sorted by Series

The decomposition of the reduction of a Deligne--Lusztig character as a sum of Weyl modules is given by Jantzen's formula. In the case of $SL_2(F_q)$ the formula can be proved by a direct computation, and as a result we will see that the entries in...

The modular representation theory of a finite group naturally breaks into different pieces called blocks, and the defect of a block is a sort of measure of its complexity. I will recall some basic aspects of this theory, and then give the complete...

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...

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...

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...

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...

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...

Last week, Ben explained how diagrammatic algebra helps understand tilting characters. In Ben's talk the diagrammatic algebra was that of Temperley-Lieb flavour and its higher rank cousins (webs etc.) I will briefly recall the diagrammatics for the...

In this talk, we will put together all ingredients we have seen in the last couple of talks to describe the algorithm to calculate tilting characters for reductive algebraic groups in the anti-spherical module. We will try to illustrate the most...

In this talk we will present two perspectives on the p-Kazhdan-Lusztig basis and its combinatorics, giving a glimpse of its complexity. This talk does not provide many answers, but will hopefully raise many interesting questions and is based on...

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...

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...

In the last talk of this series, we discuss the microlocal criterion for regular singularities of a D-module, and the existence of special filtrations on regular holonomic microdifferential modules. This allows us to define a D-module-theoretic...

I will start by recalling the notion of microlocal perverse sheaves and then briefly explain meldings. The rest of the talk is devoted to explaining the ideas involved in the proof of the codimension-three conjecture.

I will present a finite-dimensional quiver algebra whose representations are equivalent to the category of Schubert-constructible perverse sheaves on the Grassmannian $Gr(k,n)$. The functor inducing the equivalence is constructed by analyzing the...

I'll review results and examples of the invariance and monodromy of microlocal sheaves under mutations of their support. Then I'll suggest some problems in geometric representation theory where we would like to apply such techniques.

I'll discuss joint work with Zhiwei Yun constructing a natural functor from the automorphic category of a nodal curve to the automorphic category of a smoothing. The results depend on the microlocal geometry of sheaves with nilpotent singular...