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 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.
Grants and Projects
Past grants
Editorial board
I am on the editorial board of the International Journal of Algebra and Computation.
PhD Projects
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 onerelator monoids (with B. Steinberg)
Selecta Mathematica, New Series Vol. 28, 59 (2022).
 New results on the prefix membership problem for onerelator groups (with I. Dolinka)
Transactions of the American Mathematical Society Vol. 374, 2021, pp. 4309–4358.
 Undecidability of the word problem for onerelator inverse monoids via rightangled Artin subgroups of onerelator 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. 401432.

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. 419455.

Groups Acting on Semimetric Spaces and Quasiisometries of Monoids
(with M. Kambites)
Transactions of the American Mathematical Society Vol. 365, 2013, pp. 555578.

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. 9971018.

On Maximal Subgroups of Free Idempotent Generated Semigroups
(with
N. Ruskuc)
Israel Journal of Mathematics Vol. 189, 2012, pp. 147176.