I work on the representation theory of reductive groups over finite rings, such as quotients of rings of integers of local fields. I am interested in a generalisation of Deligne-Lusztig theory to this setting, as well as purely algebraic (non-cohomological) constructions of representations, and their relations to supercuspidal representations of p-adic groups.
I also work on representation zeta functions of nilpotent and compact p-adic groups. In addition, I have done some work on group schemes over local rings, and commutators in matrix rings.
Together with Andrew Lobb I am organising the British Mathematical Colloquium 2017 in Durham.
A recent workshop I co-organised: "Interactions between algebra, coding theory and cryptography".
Up to date electronic versions of my published papers can be found at the Durham Research Online repository.
- (with S. Stevens) The regular representations of GL_N over finite local principal ideal rings arXiv:1611.04796, (submitted).
- Commutators of trace zero matrices over principal ideal rings arXiv:1607.07205, (submitted).
- (with Z. Chen) The algebraisation of higher Deligne--Lusztig representations arXiv:1604.01615, (submitted).
- Representations of GL_N over finite local principal ideal rings - an overview to appear in Contemp. Math., Proceedings of the conference "Around Langlands Correspondences".
- (with C. Voll) Representation zeta functions of some
nilpotent groups associated to prehomogeneous vector
spaces arXiv:1505.06837, to appear in Forum
- Similarity and commutators of matrices over principal ideal rings Trans. Amer. Math. Soc., 368 (2016), 2333-2354.
- (with C. Voll) Representation zeta functions of
nilpotent groups and generating functions for Weyl
groups of type B
Amer. J. Math., 136(2) (2014), 501-550.
- (with C. Voll) A new statistic on the hyperoctahedral groups Electron. J. Combin., 20(3) (2013), #P50 (23 pages).
- Reductive group schemes, the Greenberg functor, and associated algebraic groups J. Pure Appl. Algebra, 216 (2012), 1092-1101. (For errata, see here)
- Extended Deligne-Lusztig varieties for general and special linear groups Adv. Math., 226 (2011), 2825-2853.
- (with A.-M. Aubert, U. Onn and A. Prasad) On cuspidal representations of general linear groups over discrete valuation rings Israel J. Math., 175 (2010), 391-420.
- The smooth representations of GL_2(o) Comm. Algebra, 37 (2009), 4416-4430.
- Unramified representations of reductive groups over finite rings Represent. Theory 13 (2009), 636-656.
368 (2016), 2333-2354
368 (2016), 2333-2354
- Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties, math.RT/0403487.
- Representations of reductive groups over quotients of local rings, math.RT/0311243.