PhD Studentship: Categorification and the Local Langlands Correspondence

Primary Supervisor: Professor Shaun Stevens

The representation theory of p-adic groups has been a highly active area of research over the last fifty years, motivated by the Local Langlands Correspondence/Conjectures and its deep connections to Number Theory. To begin with, only irreducible representations with complex coefficients were considered but, more recently, representations with coefficients in other rings or fields have been studied also. Moreover, to gain a better understanding, more importance has been given to trying to match the (derived) structures of categories on the two sides of the correspondence.

On the other hand, techniques from higher representation theory give a way to study these categories: for representations of p-adic general linear groups, this leads to a 2-representation of a certain quantum group – this is an example of a categorification of this quantum group, in which we understand its elements as functors. An analogue of this result is already known for finite general linear groups, and the project will begin by making this precise in the p-adic case. It will then aim to transfer information obtained by studying this 2-representation across the local Langlands correspondence, possibly by extending it to the relevant derived categories.

The project will be co-supervised by Shaun Stevens and Vanessa Miemietz.

Entry Requirements

The minimum entry requirement is a 2:1 bachelor's degree in mathematics.

Start Date: 1 February 2027

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