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".


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

  • 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.

  • Representations of GL_N over finite local principal ideal rings - an overview
  • (submitted).

  • (with C. Voll) Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces arXiv:1505.06837, to appear in Forum Math.

  • 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.


  • 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.