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 board of 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 publications

• Maximal subgroups of finitely presented special inverse monoids (with M. Kambites)
  Journal of the European Mathematical Society (JEMS), to appear (2024).
  
• 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.
  
• Amenability and geometry of semigroups (with M. Kambites)
  Transactions of the American Mathematical Society Vol. 369, 2017, pp. 8087–8103.
  
• On regularity and the word problem for free idempotent generated semigroups (with I. Dolinka and N. Ruskuc)
  Proceedings of the London Mathematical Society Vol. 114, 2017, pp. 401-432.
  
• Maximal subgroups of free idempotent generated semigroups over the full linear monoid (with I. Dolinka)
  Transactions of the American Mathematical Society Vol. 366, 2014, pp. 419-455.
  
• Groups Acting on Semimetric Spaces and Quasi-isometries of Monoids (with M. Kambites)
  Transactions of the American Mathematical Society Vol. 365, 2013, pp. 555-578.
  
• Maximal subgroups of free idempotent generated semigroups over the full transformation monoid (with N. Ruskuc)
  Proceedings of the London Mathematical Society Vol. 104, 2012, pp. 997-1018.
  
• On Maximal Subgroups of Free Idempotent Generated Semigroups (with N. Ruskuc)
  Israel Journal of Mathematics Vol. 189, 2012, pp. 147-176.