### Research

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.

Andrea Vera Gajardo is working with me as a postdoc in Durham until 15 Dec 2016.

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".

### Papers

Up to date electronic versions of my published papers can be found at the Durham Research Online repository.

- (with Z. Chen)
*The algebraisation of higher Deligne--Lusztig representations,*arXiv:1604.01615. - (with C. Voll)
*Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces*, arXiv:1505.06837, submitted.

*Similarity and commutators of matrices over principal ideal rings*, Trans. Amer. Math. Soc.,**368**(2016), 2333-2354.

**368**(2016), 2333-2354**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.

### Unpublished

*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.