research

Publications

- Uniform Roe algebras of uniformly locally finite metric spaces are rigid, with Florent Baudier, Bruno de Mendonça Braga, Ilijas Farah, Alessandro Vignati and Rufus Willett, to appear in Invent. Math. (2022).

- A characterisation of virtually free groups via minor exclusion, to appear in Int. Math. Res. Notices (2022).

- On the structure of asymptotic expanders, with Kang Li, Federico Vigolo and Jiawen Zhang, Adv. Math. 393 (2021).

- Expander graphs and where to find them, Oberwolfach Snapshot, to appear.

- Box spaces: geometry of finite quotients, with Alain Valette, to appear in Analysis and Geometry on Graphs and Manifolds Conference Proceedings

- Coarse fundamental groups and box spaces, with Thiebout Delabie, Proc. R. Soc. Edinb. A (2019).

- Espaces et groupes non exacts admettant un plongement grossier dans un espace de Hilbert, d'après Arzhantseva, Guentner, Osajda et Spakula, Séminaire Bourbaki 2018, to appear in Astérisque.

- Box spaces of the free group that neither contain expanders nor embed into a Hilbert space, with Thiebout Delabie, Adv. Math. 336 (2018).

- Expanders and box spaces, with Alain Valette, Adv. Math. 314 (2017).

- Embeddable box spaces of free groups, Math. Ann. 360 (2014).

- Box spaces, group extensions and coarse embeddings into Hilbert space, J. Funct. Anal. 263 (2012).

- Expanders and property A, with Nick Wright, Algebr. Geom. Topol. 12 (2012).

Preprints and misc.

- On wall structures and coarse embeddings, expository article for the Metric Embeddings: Constructions and Obstructions Fall School at IHP, Paris.

- Embeddability of generalized wreath products and box spaces, with Chris Cave and Dennis Dreesen (2013).

Theses

- Coarse Geometry and Groups, PhD Thesis (supervisor: Graham Niblo), University of Southampton (2012).

- Groups of Polynomial Growth, Part III Essay (supervisor: Ben Green), University of Cambridge (2008).