I studied Mathematics as an undergraduate at Gonville and Caius College, Cambridge, and did my PhD at King's College London, under the supervision of Prof. Colin Bushnell. After postdoctoral positions in Paris and Münster, and a junior position in Oxford, I joined UEA in 2002.

My research is at the interface of Algebra and Number Theory, in an area known as the local Langlands correspondence. In 2009 I was awarded a five-year EPSRC Leadership Fellowship on “Explicit Correspondences in Number Theory” to work in this area.

I have taught most of the core pure mathematics modules at the UEA, as well as more advanced modules in Algebra and Number Theory. I have supervised, either jointly or solely, ten PhD students to completion and several postdoctoral researchers.

I am on the EPSRC Peer Review College and was formerly co-editor of the Bulletin of the London Mathematical Society (2009-14). I was previously the Head of School of Mathematics at UEA (2015-16, 2017-21).

Website: http://archive.uea.ac.uk/~h008/

PhD opportunities in Mathematics should be on the School of Mathematics website but please also feel free to email me to discuss projects and sources of funding.

• Apr 2010–Mar 2015, EPSRC Leadership Fellow, University of East Anglia.
• Aug 2010–, Professor in Pure Mathematics, University of East Anglia.
• Aug 2007–Jul 2010, Reader in Pure Mathematics, University of East Anglia.
• Sep 2002–Jul 2007, Lecturer in Pure Mathematics, University of East Anglia.
• Oct 2000–Aug 2002, Junior Lecturer in Mathematics, Oxford University and Merton College.
• Jan 2000–Sep 2002, Postdoctoral Researcher, Westfälische Welhelms-Universität, Münster, Germany.
• Jan 1999–Dec 1999, Postdoctoral Researcher, Université de Paris-Sud, Orsay, France.

The main focus of my research is at the interface of two areas of Pure Mathematics: Representation Theory, which seeks to understand groups via their actions on vector spaces - that is, to see the different ways in which abstract groups can be thought of as matrix groups; and Number Theory, which seeks, amongst other things, to understand the integers, the rational numbers, and numbers which are roots of integer polynomials. The bridge which joins these two areas is given by the Langlands Correspondence, which is actually a broad web of (mostly) conjectures connecting global fields (for example, finite extensions of the rationals) to the representation theory of certain groups (more precisely, to automorphic representations).  

My research has concentrated on understanding the Representation Theory side of this correspondence (or rather, a local version of it) in a very explicit way, the hope being that this may eventually allow one to make the correspondence explicit. This has already been done in many cases for the full group of invertible matrices; however, for other groups, notably the orthogonal and symplectic groups, although the correspondence is now known to exist, there is no explicit version.

RESEARCH KEYWORDS:

Number Theory; Representation theory; representations of p-adic groups; local Langlands conjectures; Hecke algebras; buildings.