Research

I work in noncommutative algebra and representation theory.

I am interested in noncommutative rings that arise from the p-adic Langlands programme. In particular I am interested in properties of (mod p) Iwasawa algebras and their generalisations, consequences for smooth representations, and connections to the (mod p) p-adic Langlands programme.

I am also interested in infinite-dimensional Lie algebras and their representations, via study of universal enveloping algebras and related rings.

Publications and preprints

The canonical dimension of modules for Iwasawa algebras, submitted, arXiv:2306.09696.

Let F be a non-trivial finite extension of the p-adic numbers, and G be a compact p-adic Lie group whose Lie algebra is isomorphic to a split simple F-Lie algebra. We prove that the mod p Iwasawa algebra of G has no modules of canonical dimension one. One consequence is a new upper bound on the Krull dimension of the Iwasawa algebra. We also prove a canonical dimension-theoretic criterion for a mod p smooth admissible representation to be of finite length. Combining our results shows that any smooth admissible representation of GL_n(F), with central character, has finite length if its dual has canonical dimension two.

Coherence of augmented Iwasawa algebras, Adv. Math. 417, no. 108916, (2023). journal, arxiv, pdf

The augmented Iwasawa algebra of a p-adic Lie group is a generalisation of the Iwasawa algebra of a compact p-adic Lie group. We prove that a split-semisimple group over a p-adic field has a coherent augmented Iwasawa algebra if and only if its root system is of rank one. We deduce that the general linear group of degree n has a coherent augmented Iwasawa algebra precisely when n is at most two. We also characterise when certain solvable p-adic Lie groups have a coherent augmented Iwasawa algebra.

Some recent talks

Coherent rings and where to find them - Algebra Seminar, University of Manchester, April 2024
Canonical dimension for mod p representations of p-adic Lie groups - Arithmetic Study Group (Algebra & Number Theory Seminar), University of Durham, January 2024
Canonical dimension and Iwasawa algebras - Workshop in Noncommutative Algebra and Representation Theory, University of Kent, July 2023
The augmented Iwasawa algebra - Focused Research Event on Smooth representations of GL(n, Qp) in natural characteristic, University of Oxford, July 2022
Dimensions of Iwasawa algebras and their representations - Algebra Seminar, University of Oxford, January 2022
Krull dimension of some Iwasawa algebras - Algebra Seminar, University of Manchester, November 2021