Research

The main focus of my research is on the representation theory of p-adic classical groups. The idea is to understand the representations of these groups in a very explicit way in the hope that this will give us arithmetic information via the (for now, mostly conjectural) Langlands correspondence. I will hopefully write more about this one day. In the meantime, see my publications/preprints, in particular, the recent papers:

• on exhaustion for the supercuspidal representations of p-adic classical groups [Invent. Math.];
• on exhaustion for the supercuspidal representations of the multiplicative group of p-adic central simple algebras (with Vincent Sécherre, Marseille) [J. Inst. Math. Jussieu];
• on epsilon factors of pairs for p-adic general linear groups (with Vytautas Paškūnas, Bielefeld) [Amer. J. Math.];
• on genericity of supercuspidal representations of Sp(4) (with Corinne Blondel, Paris 7) [Compos. Math.];
• and on covers for the self-dual supercuspidal representations of the Siegel Levi subgroup in p-adic classical groups (with David Goldberg, Purdue, and Phil Kutzko, Iowa) [IMRN].

If you would like to see some work in progress then please click here.

In the autumn of 2007, we had a small group of people working on the representation theory of p-adic groups:

• Alberto Minguez (Aug 2007-Jan 2008),
• Michitaka Miyauchi (Oct 2007-Apr 2008),
• Vincent Sécherre (Oct-Nov 2007),

and myself, all funded through my EPSRC grant. We are running a study group on representations of unitary groups, the aim of which is to end with something for the Paris automorphic forms book project. See here for more details on the study group.

I am part of the Number Theory, Ergodic Theory and Dynamical Systems research group, along with Graham Everest, Anish Ghosh and Tom Ward. We have worked together on the appearance of primitive prime divisors in certain recurrence sequences and with Richard Miles, on analogues of the Prime Number Theorem and Mertens' Theorem for non-hyperbolic algebraic dynamical systems. I don't really understand any of this so, to read more about these sorts of questions, I suggest you look at Tom Ward's Ergodic Theory page.

Graham Everest and I also worked, with Valéry Mahé (now Université de Franche-Comté), on the appearance of prime terms in Elliptic Divisibility Sequences (EDS). See Graham Everest's webpage for more information about EDS.

In the autumn of 2007, Valéry organised a study group on some papers of Bugeaud, Mignotte and Siksek, as part of our Arithmetic and Dynamics seminar.