### 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

My papers can be found on arXiv and on the Durham Research Online repository. The arXiv versions are often, but not always, identical to the published versions.

*Rationality of representation zeta functions of compact p-adic analytic groups*

arXiv:2007.10694, 56 pages, submitted.

*Representations of*SL

*_n over finite local rings of length two*

**566**(2021), 119-135.

*A uniform proof of the finiteness of the class group of a global field*

arXiv:1909.07121, to appear in Amer. Math. Monthly.

*Representations of reductive groups over finite local rings of length two*

J. Algebra,

**525**(2019), 171-190.

*Representation growth of compact linear groups*

**372(2)**(2019), 925–980.

*Commutators of trace zero matrices over principal ideal rings*

**228**

**(1)**(2018), 211–227.

*The regular representations of*GL

*_N over finite local principal ideal rings*

**49**(2017), 1066-1084.

*The algebraisation of higher Deligne—Lusztig representations*

**23(4)**(2017), 2907-2926. Open Access.

*Representations of*GL

*_N over finite local principal ideal rings - An overview*

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

*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*

*Trans. Amer. Math. Soc.,*

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

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

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

*Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type*B

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

*A new statistic on the hyperoctahedral groups*

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

*J. Pure Appl. Algebra,*

*Reductive group schemes, the Greenberg functor, and associated algebraic groups*

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

*Adv. Math.,*

*Extended Deligne-Lusztig varieties for general and special linear groups*

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

*On cuspidal representations of general linear groups over discrete valuation rings*

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

*Comm. Algebra,*

*The smooth representations of*GL_2(o)

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

*Represent. Theory*

*Unramified representations of reductive groups over finite rings*

**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.