The nilCoxeter algebras and their cohomology

Pre-talk Title: Calculating cohomology.

Abstract: I'll talk about how to calculate cohomology of finite dimensional algebras, especially self-injective algebras, and what it's good for.

Title talk: The nilCoxeter algebras and their cohomology.

Abstract talk: Given a Coxeter group, there is an associated nilCoxeter algebra given by replacing the generators squaring to one by generators squaring to zero, but keeping the remaining braid relations. This is a local algebra, so it makes sense to ask for the structure of Ext of the trivial module. This is a very interesting non-commutative semiprime polynomial identity ring given by explicit generators and quadratic relations. It's related to some groups called cactus groups, via Koszul duality.