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 increasingly interested in properties of infinite groups which allow one to approximate them by finite groups, including residual finiteness; local embeddability and soficity.

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 and preprints

- Controlling LEF growth in some group extensions 2022
- Quantifying lawlessness in finitely generated groups 2021
- Topological full groups of minimal subshifts and quantifying local embeddings into finite groups with Daniele Dona, 2021
- Quantifying local embeddings into finite groups 2021
- Short Laws for Finite Groups of Lie Type with Andreas Thom, 2018
- Navigating Directed Cayley Graphs of Small Diameter: A Potent Solovay-Kitaev Procedure International Journal of Algebra and Computation, Volume 29, no. 7 (2019), pp. 1319-1342
- Uniform Diameter Bounds in Branch Groups 2017
- Short Laws for Finite Groups and Residual Finiteness Growth with Andreas Thom, Transactions of the AMS, Volume 371 (2019), pp. 6447-6462
- Expansion, Random Walks and Sieving in $SL_2(\mathbb{F}_p[t])$ Israel Journal of Mathematics, Volume 215 (2016), pp. 559-582
- New Uniform Diameter Bounds in Pro-$p$ Groups Groups, Geometry and Dynamics, Volume 12, Issue 3 (2018) pp. 803-836

### Teaching

In Lent Term 2022 I shall be lecturing Part III Infinite Groups. Supporting materials, including lecture notes and example sheets, shall appear here in the fullness of time. In the meanwhile, see here for some introductory notes covering material which will be prerequisite for the course.