Research

My mathematical research interests are in the general area of geometric and combinatorial group theory, including but not limited to word growth, conjugacy growth, equations, power series, virtually abelian groups, nilpotent groups, formal languages and automata, decision problems, model theory of groups.

Publications

• On groups with EDT0L word problem, with Alex Bishop, Murray Elder, Paul Gallot, and Alex Levine [Internat. J. Agebra Comput. (Online Ready 2026)] [arXiv]
• Twisted conjugacy growth series of virtually abelian groups, with Maarten Lathouwers [Bull. London Math. Soc., 57: 3490-3510.] [arXiv]
• Effective equation solving, constraints and growth in virtually abelian groups, with Laura Ciobanu and Alex Levine [SIAM J. Appl. Algebra Geom. 9 (2025), no. 1, 235–260] [arXiv]
• Conjugacy Class Growth in Virtually Abelian Groups, with Aram Dermenjian [J. Groups Complex. Cryptol. 17 (2025), no. 1, Paper No. 1, 14 pp.] [arXiv]
• Rational sets in virtually abelian groups: languages and growth, with Laura Ciobanu [Enseign. Math. 71 (2025), no. 3/4, pp. 231–260] [arXiv]
• Solving equations in the solvable Baumslag-Solitar groups using EDT0L systems, with Andrew Duncan, Derek F. Holt, and Sarah Rees [Journal of Algebra 630 (2023) 434-456] [arXiv]
• Conjugacy growth in the higher Heisenberg groups [Glasgow Mathematical Journal. 2023;65(S1):S148-S169.] [arXiv]
• Equations in virtually abelian groups: languages and growth, with Alex Levine [Internat. J. Algebra Comput. 32, no. 3, 411-442 (2022)] [arXiv]
• The conjugacy growth of the soluble Baumslag-Solitar groups, with Laura Ciobanu and Turbo Ho [New York J. Math. 26 (2020) 473-495] [arXiv]
• Rational growth in virtually abelian groups [Illinois J. Math. 63 (2019), no. 4, 513-549] [arXiv]

Thesis

You can find my PhD thesis, ‘Aspects of growth in finitely generated groups’, here.