Representation theory and Categorification

About the Project

Primary Supervisor: Prof Vanessa Miemietz

Categorification has led to major advances in representation theory in the last 30 years, including the proof of Broué’s abelian defect group conjecture for symmteric groups and the proof of the Kazhdan—Lusztig conjectures for all Coxeter types.

Classically, a representation of an algebra (a ring that is also a vector space) is an action of the latter on a vector space via linear maps. This is categorified to an action of a monoidal category on another category (or, more generally, of a 2-category on a collection of categories) via (nice) functors. This yields new information by looking at natural transformations between such functors.

This project will study specific examples of such categorifications.

Entry Requirements

The minimum entry requirement is 2:1 in mathematics.

Mode of Study

Full or Part time

Start Date:

1 October 2026