## Matthew TointonI am a post-doctoral researcher in mathematics working with Alain Valette at the Université de Neuchâtel, Switzerland. I tend to be interested in problems and results that involve some combination of algebra, combinatorics and geometry; much of my work lies at the interface between additive combinatorics and geometric group theory. I completed my PhD in Cambridge in 2013 under the supervision of Ben Green. Before starting my current position I was a Junior Research Fellow at Homerton College, Cambridge, and a post-doc at Université Paris-Sud. |

In reverse chronological order:

- The Mahler conjecture in two dimensions via the probabilistic method, to appear in
*Amer. Math. Monthly*, 9pp. arXiv - Some results on the probability that two elements of an amenable group commute, submitted, 14pp. arXiv
- The asymptotic dimension of box spaces of virtually nilpotent groups (with Thiebout Delabie), submitted, 7pp. arXiv
- Properness of nilprogressions and the persistence of polynomial growth of given degree (with Romain Tessera), submitted, 34pp. arXiv
- Horofunctions on graphs of linear growth (with Ariel Yadin),
*C. R. Math. Acad. Sci. Paris***354**(2016), 1151-1154. arXiv | Journal - Approximate subgroups of residually nilpotent groups, submitted, 12pp. arXiv
- Nilprogressions and groups with moderate growth (with Emmanuel Breuillard),
*Adv. Math.***289**(2016), 1008-1055. arXiv | Journal - Polynomials and harmonic functions on discrete groups (with Tom Meyerovitch, Idan Perl and Ariel Yadin),
*Trans. Amer. Math. Soc.***369**(2017), 2205-2229. arXiv | Journal - Characterisations of algebraic properties of groups in terms of harmonic functions,
*Groups Geom. Dyn.***10**(2016), 1007-1049. arXiv | Journal - Recurrence and non-uniformity of bracket polynomials,
*Online J. Anal. Comb.***9**(2014), 36pp. arXiv | Journal - Freiman's theorem in an arbitrary nilpotent group,
*Proc. London Math. Soc.***109**(2014), 318-352. arXiv | Journal

An alternative approach to Freiman's theorem in *p*-groups.

An essay on the Tits alternative, which I wrote in 2009 as part of my Part III studies in Cambridge.

A proof of Minkowski's second theorem, which may be helpful to people learning or lecturing that result.

Graduate student and postdoc seminar 2015/16, Université Paris-Sud