Seminars Sorted by Series

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...

The outer automorphism group of the free group Out(F_r) acts as the isometry group on the deformation space of weighted graphs, Culler-Vogtmann Outer space CV_r. The train track theory of Bestvina-Feighn-Handel bridges studying topological...

A random walk on a hyperbolic group G will converge almost surely to the boundary, defining a stationary measure at infinity. When G is a cocompact fuchsian group, this boundary is the circle, and when the random walk is finitely supported it is...

The Poisson boundary is a measure theoretic object which classifies both the space of possible asymptotic events of a random walk and the space of bounded harmonic functions. For most identifications so far a moment condition has proved crucial. I...

Artin groups are a family of groups generalizing braid groups, and are given by simple looking group presentations. In this talk, I will discuss profinite properties of Artin groups, such as residual finiteness, and the connection between the group...

The free group algebra appears often as a major tool in dealing with problems about free groups. It is also a lovely object for its own sake, featuring many analogies with the free group: for example, it satisfies an analog of the Nielsen-Schreier...

Recent progress on character bounds for groups of Lie type makes it feasible in many cases to find the asymptotic growth, for fixed q and n tending to infinity, of the number of n-dimensional representations of a Fuchsian group G over the field with...

In many groups, the optimal diameter for the solutions of the isoperimetric problem is asymptotically equivalent to the lower bound coming from their cardinality; in this situation one says that the Følner function is lossless with respect to the...