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, Giovanni Italiano, 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:

To get regular updates about GGSE, please send an email to ggse-join@ucl.ac.uk.

Abstracts and titles of previous talks are available here.

Details of our next meeting

Oxford 22 May 2026

Mathematical Institute L5

13:15 Weakly acylindrical group actions on hyperbolic spaces

Koji Fujiwara (OIST/Kyoto)

I will discuss weakly acylindrical group actions on hyperbolic spaces. I will explain that discrete actions of finitely generated groups on \(\mathbb H^n\) are weakly acylindrical in a certain uniform sense. As an application, I will discuss the uniform Tits alternative. This is joint work with Emmanuel Breuillard. As another application, I will present some uniform estimates for the drift of random walks. This is joint work with Ryokichi Tanaka.

14:30 Top-dimensional \(l^2\)-homology of hyperbolic groups

Ana Isakovic (Cambridge)

Computing \(l^2\)-homology can be a demanding task especially if one attempts to follow the definition directly. In this talk, I will speak about using automatic structures to construct top-dimensional \(l^2\)-cycles and how they can further be used to compute \(l^2\)-homology of certain hyperbolic groups.

15:30 TEA in the Common Room

16:00 Special coherent groups

Sam Fisher (ICMAT)

A conjecture of Gromov and Wise predicts that among groups of cohomological dimension two, coherence is equivalent to the vanishing of the second \(L^2\)-Betti number. In this talk we address this conjecture in the class of virtually special groups and discuss an analogue of the conjecture in higher cohomological dimension. The talk is based on joint work with Pablo Sánchez-Peralta.

Reimbursements

There is only one step to getting some money for your train tickets: Send exactly one email to l.louder AT ucl.ac.uk and I will set things in motion. Don't send an email before the meeting. I will say yes, as long as it's reasonable.