ºÚÁÏÍø´óʼÇ

Abstract

Representation theory is, at its most basic level, the study of the category of representations of a group G, written Rep(G).  Tensor categories are a natural generalisation of Rep(G), and provide a home for powerful constructions which can in turn tell us something new about Rep(G).  In the first talk, I will give a high level discussion of tensor categories with many examples, and discuss the idea of Tannakian formalism and Deligne's theorem on super-Tannakian categories over C.

In the second talk, I will focus on semisimplification, which is a construction that takes in a tensor category and outputs a semisimple quotient tensor category.  This construction comes with a functor, which has a tendency to produce interesting representation-theoretic constructions in a bevy of cases.  We will look at several examples of semisimplification, and if there's time I'll discuss recent work on the study of such functors for modular representations of the symmetric group and/or algebraic groups.