13 citations · 29 across the 17 of their papers we have counts for
14 papers · 1 filter
Residually finite groups with uniformly almost flat quotients
David Guo, Matthew Tointon
We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obta…
Balls in groups: volume, structure and growth
Romain Tessera, Matthew Tointon
We develop a fine-scale structural theory for balls of polynomial volume in finitely generated groups. Our main result shows that a polynomial-volume hypothesis on a single ball im…
Geometric amenability in totally disconnected locally compact groups
Romain Tessera, Matthew Tointon
We give a short geometric proof of a result of Soardi & Woess and Salvatori that a quasitransitive graph is amenable if and only if its automorphism group is amenable and unimodula…
Explicit universal minimal constants for polynomial growth of groups
Russell Lyons, Avinoam Mann, Romain Tessera +1
Shalom and Tao showed that a polynomial upper bound on the size of a single, large enough ball in a Cayley graph implies that the underlying group has a nilpotent subgroup with ind…
A brief introduction to approximate groups
Matthew Tointon
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
Probabilistic nilpotence in infinite groups
Armando Martino, Matthew Tointon, Motiejus Valiunas +1
The 'degree of k-step nilpotence' of a finite group G is the proportion of the tuples (x_1,...,x_{k+1}) in G^{k+1} for which the simple commutator [x_1,...,x_{k+1}] is equal to the…
Scaling limits of Cayley graphs with polynomially growing balls
Romain Tessera, Matthew Tointon
Benjamini, Finucane and the first author have shown that if (G_n,S_n) is a sequence of Cayley graphs such that |S_n^n|=O(n^D|S_n|), then the sequence (G_n,d_{S_n}/n) is relatively…
Commuting probabilities of infinite groups
Matthew Tointon
Let G be a group, and let M=(m_n) be a sequence of finitely supported probability measures on G. Consider the probability that two elements chosen independently according to m_n co…
The asymptotic dimension of box spaces of virtually nilpotent groups
Thiebout Delabie, Matthew Tointon
We show that every box space of a virtually nilpotent group has asymptotic dimension equal to the Hirsch length of that group.
Properness of nilprogressions and the persistence of polynomial growth of given degree
Romain Tessera, Matthew Tointon
We show that an arbitrary nilprogression can be approximated by a proper coset nilprogression in upper-triangular form. This can be thought of as a nilpotent version of the Freiman…
Nilprogressions and groups with moderate growth
Emmanuel Breuillard, Matthew Tointon
We show that doubling at some large scale in a Cayley graph implies uniform doubling at all subsequent scales. The proof is based on the structure theorem for approximate subgroups…
Polynomials and harmonic functions on discrete groups
Tom Meyerovitch, Idan Perl, Matthew Tointon +1
Alexopoulos proved that on a finitely generated virtually nilpotent group, the restriction of a harmonic function of polynomial growth to a torsion-free nilpotent subgroup of finit…
Characterisations of algebraic properties of groups in terms of harmonic functions
Matthew Tointon
We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group…
On harmonic functions and the linear-growth case of Gromov's theorem
Matthew Tointon
We show that the space of harmonic functions on a finitely generated infinite group G is finite dimensional if, and only if, G has a finite-index subgroup isomorphic to the integer…