Groups and Geometry in South England

This is a series of meetings, with the aim of bringing together the geometric group theorists in the South East of England. The meetings are sponsored by mathematicians from the Universities of Bristol, Cambridge, London, Oxford, Warwick, and Southampton, and organised by Martin Bridson, Mark Hagen, Robert Kropholler, Lars Louder, John Mackay, Ashot Minasyan, Saul Schleimer, Henry Wilton, and Ric Wade. We have been awarded LMS Scheme 3 funding, as well as support from the Isaac Newton Institute for Mathematical Sciences.

In 2025-26, the meetings will tentatively be as follows:

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Abstracts and titles of previous talks are available here.

Details of our next meeting

Warwick 27 March 2026

MS03 Zeeman

1:00 - 2:00 EpiC-ness of groups

Raad Al Kohli

We shall introduce the class of epiC groups. A finitely generated group G is epiC if there is a language L (belonging to class C), where for each non-trivial element of the group there is at least one representative in L and no element in L represents the identity element. We give examples of epiC groups, as well as discuss the relationship between epiC groups and various well studied classes of groups defined by formal language constraints. We also give a characterisation of having solvable word problem in the language of epiC groups. Joint with Collin Bleak and Luna Elliott.

2:15 - 3:15 Twisted Conjugacy and the R-infinity Property for Groups with Infinitely Many Ends

Harry Iveson

Given a group G and an automorphism phi of G, one may define a "phi-twisted conjugacy" relation on G. We then say that G has property R-infinity if for every automorphism of G, the determined relation partitions G into infinitely many equivalence classes. In this talk we will explore the twisted conjugacy relation, and use a result of Levitt--Lustig to show that any finitely presented group with infinitely many ends has property R-infinity. This work is joint with Francesco Fournier-Facio, Armando Martino, Wagner Sgobbi, and Peter Wong.

3:15 - 3:45 Coffee break

3:45 - 4:45 Chaos in the space of subgroups

Zachery Munro

The subgroups Sub$(G)$ of a countable group $G$ can be given a topology as a subspace of $\{0,1\}^G$ with the product topology. With this topology, Sub$(G)$ is a Polish space. Thus, the Cantor-Bendixson theorem implies a unique decomposition Sub$(G)=\mathcal K\sqcup C$ such that $\mathcal K$ is a perfect subspace, the \emph{perfect kernel}, and $C$ is countable. The conjugation action $G\curvearrowright \mathrm{Sub}(G)$ respects this decomposition, so we have an action $G\curvearrowright \mathcal K$. We concern ourselves with the topological dynamics of this action. In particular, we prove that a torsion-free cubulated hyperbolic group acts \emph{chaotically} — a notion of well-mixing — on its perfect kernel. This is joint work with Penelope Azuelos and Mark Hagen.

Reimbursements

Now that 31 December 2025 has passed our financial position is much different: we are back to LMS money only and this means that postgrads and speakers are our only priority and we cannot guarantee cover in advance for postgrads.