Groups and Geometry in the South East

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 Cambridge, London, Oxford, Warwick, and Southampton, and organised by Martin Bridson, Peter Kropholler, Lars Louder, Ashot Minasyan, Saul Schleimer, and Henry Wilton. We have been awarded LMS Scheme 3 funding.

In 2018-19, 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

Friday 26 October, 2018

Location: University College London, 25 Gordon Street, Room 706

1:30-2:30 Local maxima of the systole function

Maxime Fortier-Bourque (Glasgow)

The systole of a hyperbolic surface is the length of any of its shortest closed geodesics. Schmutz Schaller initiated the study of the systole function and its local maxima in the 90's. I will explain a construction of a new infinite family of closed hyperbolic surfaces which are local maxima for the systole. The simplest of these surfaces is the Bolza surface, which is the surface of genus 2 with the largest number of symmetries. In higher genus, we obtain super-exponentially many examples and most of them have a trivial automorphism group. This is joint work with Kasra Rafi.

2:40-3:40 Subgroups of hyperbolic groups

David Hume (Oxford)

Here there be dragons. But these dragons are not arbitrary, for instance, they have finite asymptotic dimension and therefore their Cayley graphs do not contain expanders. The purpose of this talk is to introduce new geometric invariants which quantify the statement "this Cayley graph does not contain expanders" and show that they provide new information on all finitely generated subgroups of hyperbolic groups. As an example we will use these invariants to provide a completely geometric proof that the only Baumslag-Solitar groups admitting a coarse embedding into a hyperbolic group are the virtually abelian ones.

3:40-4:00 Tea

4:00-5:00 TITLE

Ana Khukhro (Neuchâtel/Cambridge)



There is travel money available for speakers and students. Please fill out this form and send it, along with receipts, to
Lars Louder
Dept of Mathematics
University College London
Gower St