### 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.

Together with Andrew Lobb I organised the British Mathematical Colloquium 2017 in Durham.

### Papers

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*

Selecta Math. (N.S.), "Online
First". *Representations of*GL*_N over finite local principal ideal rings - An overview*
In "Around Langlands Correspondences", Contemp. Math.,
- (with C. Voll)
*Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces*Forum Math.,**29(3)**(2017), 717-734.

*Similarity and commutators of matrices over principal ideal rings*- (with C. Voll)
*Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type*B

Amer. J. Math., - (with C. Voll)
*A new statistic on the hyperoctahedral groups*
Electron. J. Combin., *Reductive group schemes, the Greenberg functor, and associated algebraic groups**Extended Deligne-Lusztig varieties for general and special linear groups*- (with A.-M. Aubert, U. Onn and A. Prasad)
*On cuspidal representations of general linear groups over discrete valuation rings*
Israel J. Math., *The smooth representations of*GL_2(o)*Unramified representations of reductive groups over finite rings*

**691**(2017), 337-358.

*Trans. Amer. Math. Soc.,*

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

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

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

**136(2)**(2014), 501-550.

**20(3)**(2013), #P50 (23 pages).

*J. Pure Appl. Algebra,*

**216**(2012), 1092-1101. (errata)

*Adv. Math.,*

**226**(2011), 2825-2853.

**175**(2010), 391-420.

*Comm. Algebra,*

**37**(2009), 4416-4430.

*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.