Program

The conference will consist of two mini-courses, one featured lecture and 17 contributed talks by the participants. You can find the speakers and abstracts below.

Mini-courses

Introduction to the modular representation theory of finite groups

Speaker : Jun.-Prof. Dr. Caroline Lassueur (TU Kaiserslautern.)

Abstract :
Modular representation theory is the study of representations of groups and related algebras over fields of positive characteristic. It was initially developed by R. Brauer, with a view towards the structure of finite groups. The aim of this mini-course is two-fold: first, provide the student with an introduction to this topic with a focus on finite groups, and second, investigate the connections between ordinary and modular representation theory.

The first part of the course we will review basic notions of representation theory: representations, characters, the group algebra and its modules, modular systems, Brauer characters, decomposition matrices, the theory of vertices and sources, block algebras.

The second part will focus on current research problems in block theory. We will investigate different types of categorical equivalences between blocks of finite groups and describe their numerical and group-theoretical invariants. Finally, we will review fundamental open problems and deep conjectures moving the topic forward.


Schur-Weyl duality and categorification

Speaker : Dr. Christopher Bowman (University of York).

Abstract :
Schur—Weyl duality relates Hecke and (affine) Lie algebras through mutually centralising actions on tensor space. The resulting centraliser algebras are important in knot theory and arise as transfer-matrix-algebras in statistical mechanics.

Recently, this phenomenon has been lifted to a higher categorical level which incorporates richer, graded structures on these algebras. This series of lectures will focus on the simplest case of (affine) sl2 — here the resulting centraliser algebras are known as the Temperley—Lieb algebras of types A and B.

We will explicitly focus on these algebras from several points-of-view: (1) invariant theoretic diagrammatic algebras (2) quotients of Hecke algebras (3) quotients of KLR algebras and (4) endomorphism algebras of Soergel-bimodules.

Featured lecture

On maximal embeddings of finite quasisimple groups

Speaker : Prof. Gerhard Hiss (RWTH Aachen).

Abstract
:
Let S be a finite non-abelian simple group and let R(S) denote the smallest degree of a non-trivial projective representation of S. This gives rise to an embedding of a quasisimple covering group G of S into a classical group X. If X is as small as possible, then, up to a few exceptions, NX(G) is a maximal subgroup of X.

 

Contributed talks

You can find a complete list of the abstracts, including the contributed talks, below.