I am a Fellow and College Teaching Officer at Christ’s College Cambridge, and a member of the University of Cambridge’s Department of Pure Mathematics and Mathematical Statistics.
My area of research is asymptotic group theory. I am interested in a range of questions concerning constructions of expander graphs; diameters of Cayley graphs; word maps on groups and random walks. I am also interested in properties of infinite groups which allow one to approximate them by finite groups, including residual finiteness; LEF and soficity. You can watch a lecture I gave in November 2025 about some of my recent theorems here.
From 2016 to 2019 I was a postdoctoral research assistant at the University of Göttingen, where I worked in the research group of of Prof. Harald Andrés Helfgott. I completed my DPhil at the University of Oxford in 2015, under the supervision of Prof. Marc Lackenby.
Outside mathematics I am a music-lover; a jogger, and a collector of postcards.
Publications
- Non-solutions to mixed equations in acylindrically hyperbolic groups coming from random walks, with Alessandro Sisto, Archiv der Mathematik (2026)
- Controlling LEF growth in some group extensions, Journal of Algebraic Combinatorics (2026)
- On the spectrum of residual finiteness growth functions, Journal of Pure and Applied Algebra (2025)
- The length of mixed identities for finite groups, with Jakob Schneider and Andreas Thom, Journal of Algebra 670 (2025): 13-47
- Hopfian wreath products and the stable finiteness conjecture with Francesco Fournier-Facio, Mathematische Zeitschrift 308 (2024)
- On the length of non-solutions to equations with constants in some linear groups, with Jakob Schneider and Andreas Thom, Bulletin of the London Mathematical Society 56.7 (2024): 2338-2349
- Short Laws for Finite Groups of Lie Type with Andreas Thom, Journal of the European Mathematical Society (2024): DOI 10.4171/JEMS/1547
- Local permutation stability Groups, Geometry and Dynamics (2024): DOI 10.4171/GGD/827
- Quantifying lawlessness in finitely generated groups Journal of Group Theory 27.1 (2024): 31-59
- Topological full groups of minimal subshifts and quantifying local embeddings into finite groups with Daniele Dona, Ergodic Theory and Dynamical Systems 43.5 (2023): 1492-1510
- Quantifying local embeddings into finite groups Journal of Algebra, Volume 608 (2022): 214-238
- Navigating Directed Cayley Graphs of Small Diameter: A Potent Solovay-Kitaev Procedure International Journal of Algebra and Computation, Volume 29, no. 7 (2019): 1319-1342
- Short Laws for Finite Groups and Residual Finiteness Growth with Andreas Thom, Transactions of the AMS, Volume 371 (2019): 6447-6462
- Expansion, Random Walks and Sieving in $SL_2(\mathbb{F}_p[t])$ Israel Journal of Mathematics, Volume 215 (2016): 559-582
- New Uniform Diameter Bounds in Pro-$p$ Groups Groups, Geometry and Dynamics, Volume 12, Issue 3 (2018): 803-836
Preprints
- Co-intersection graphs of nonabelian finite simple groups have diameter two, with Kamilla Rekvényi, 2026
- Mixed identities for simple locally finite groups, with Kivanç Ersoy, Jakob Schneider and Andreas Thom, 2026
- Groups with arbitrarily poor permutation stability, 2026
- Sofic actions, halo products, and metric approximations of groups, with Vadim Alexeev, 2026
- Groups of arbitrary lawlessness growth, with Jacob Willis, 2025
- Non-singular word maps for linear groups, with Jakob Schneider and Andreas Thom, 2023
- Uniform Diameter Bounds in Branch Groups, 2017
PhD students
Jacob Willis (October 2024 – present)
Jakub Tucker (October 2025 – present)
Work by my summer research students
Residual finiteness of graph wreath products (undergraduate research project by Amy Needham, summer 2025)
Uniform Directed and Undirected Diameter Bounds in GGS Groups (undergraduate research project by Pascal Economou, Summer 2022)
Topics in asymptotic group theory (undergraduate research project by Segev Gonen Cohen, Summer 2021)
Teaching
Part IB Linear Algebra (Michaelmas Term 2024):
Part III Infinite Groups (Lent Term 2022):
