Matthew Tointon

I 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.

Papers and preprints

In reverse chronological order:

  1. Scaling limits of Cayley graphs with polynomially growing balls (with Romain Tessera), 37pp.     arXiv
  2. The Mahler conjecture in two dimensions via the probabilistic method, to appear in Amer. Math. Monthly, 9pp.     arXiv
  3. Commuting probability of infinite groups, submitted, 20pp.     arXiv
  4. The asymptotic dimension of box spaces of virtually nilpotent groups (with Thiebout Delabie), to appear in Discrete Math., 7pp.     arXiv
  5. Properness of nilprogressions and the persistence of polynomial growth of given degree (with Romain Tessera), submitted, 34pp.     arXiv
  6. Horofunctions on graphs of linear growth (with Ariel Yadin), C. R. Math. Acad. Sci. Paris 354 (2016), 1151-1154.     arXiv    |    Journal
  7. Approximate subgroups of residually nilpotent groups, submitted, 12pp.     arXiv
  8. Nilprogressions and groups with moderate growth (with Emmanuel Breuillard), Adv. Math. 289 (2016), 1008-1055.     arXiv    |    Journal
  9. 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
  10. Characterisations of algebraic properties of groups in terms of harmonic functions, Groups Geom. Dyn. 10 (2016), 1007-1049.     arXiv    |    Journal
  11. Recurrence and non-uniformity of bracket polynomials, Online J. Anal. Comb. 9 (2014), 36pp.     arXiv    |    Journal
  12. Freiman's theorem in an arbitrary nilpotent group, Proc. London Math. Soc. 109 (2014), 318-352.     arXiv    |    Journal


Emmanuel Breuillard, Thiebout Delabie, Tom Meyerovitch, Idan Perl, Romain Tessera, Ariel Yadin.

Unpublished material

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