REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Justin Greenough

ABSTRACT: Many classical algebraic structures have higher-dimensional analogues which can be understood from the standpoint of category theory. In particular the theory of rings and modules has a beautiful categorification. In this talk I will discuss categorified versions of structures such as the tensor product and centre, and will show that many familiar classical formulae reappear in the categorified theory. Primary applications will include results in the representation theory of finite groups, and in the theory of categorical group actions.