I am a Professor of Mathematics and an EPSRC Research Fellow working in the School of Mathematics of the University of East Anglia.

I am an algebraist with interests in a broad range of topics including: combinatorial and geometric group and semigroup theory, algorithmic problems in algebra, decidability, homological finiteness properties, algebraic combinatorics, and groups and monoids acting on graphs, relational structures, and topological spaces.


I am on the editorial boards of the following journals:

• Journal of the London Mathematical Society
• Bulletin of the London Mathematical Society, and the
• International Journal of Algebra and Computation.

If you are interested in working with me as a PhD student or postdoc, please get in touch with me.

Selected recent publications

• Maximal subgroups of free projection- and idempotent-generated semigroups with applications to partition monoids (with J. East, P. A. Azeef Muhammed and N. Ruskuc)
  Proceedings of the London Mathematical Society, to appear (2026).
  [Preprint from arXiv]
• Magnus submonoids and membership problems in one-relator, surface and hyperbolic groups (with I. Foniqi)
  Transactions of the American Mathematical Society, to appear (2026).
  [Preprint from arXiv]
• Two-sided homological properties of special and one-relator monoids (with B. Steinberg)
  Forum of Mathematics, Sigma, (2026), Vol. 14:e58 1-23
  [Preprint from arXiv] [Final published journal version]
• Membership problems in braid groups and Artin groups (with C.-F. Nyberg-Brodda)
  Journal of the London Mathematical Society, (2025), Vol. 112:e70326.
  [Preprint from arXiv] [Final published journal version]
• Maximal subgroups of finitely presented special inverse monoids (with M. Kambites)
  Journal of the European Mathematical Society (JEMS), to appear (2025).
  
• Projection algebras and free projection- and idempotent-generated regular $*$-semigroups (with J. East, P. A. Azeef Muhammed and N. Ruskuc )
  Advances in Mathematics, Vol. 473, July 2025, 110288.
  
• Prefix monoids of groups and right units of special inverse monoids (with I. Dolinka)
  Forum of Mathematics, Sigma Vol. 11:e97 1–19, (2023).
  [Preprint from arXiv] [Final published journal version]
• A Lyndon's Identity theorem for one-relator monoids (with B. Steinberg)
  Selecta Mathematica, New Series Vol. 28, 59 (2022).
  
• New results on the prefix membership problem for one-relator groups (with I. Dolinka)
  Transactions of the American Mathematical Society Vol. 374, 2021, pp. 4309–4358.
  
• Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups.
  Inventiones Mathematicae Vol. 219, 2020, pp. 987–1008.
  
• On cogrowth, amenability and the spectral radius of a random walk on a semigroup (with M. Kambites)
  International Mathematics Research Notices (IMRN) Vol. 2020, No. 12, pp. 3753–3793.