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, and Henry Wilton. We have been awarded LMS Scheme 3 funding, as well as support from the Isaac Newton Institute for Mathematical Sciences.

In 2024-25, 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

Bristol 7 February 2025

Room 2.04 Fry Building

1:15-2:15 Curve graphs and finite-type Artin groups

Kaitlin Ragosta (Brandeis)

Finite-type Artin groups were first defined as generalizations of braid groups, and many of the techniques used to study these groups were developed by generalizing combinatorial tools originally used to study braid groups. Since braid groups are also mapping class groups, it is reasonable to ask if some of the more geometric methods for studying mapping class groups could also be extended to finite-type Artin groups. In this talk, I will define a generalization of the curve graph for finite-type Artin groups, discuss its similarities with the classical version, and explain what this can tell us about finite-type Artin groups.

2:30-3:30 On automorphisms of graphs of groups with cyclic edge groups

Ilya Kazachkov (UPV/EHU)

We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when centralisers of elements in the vertex groups, and the edge groups are infinite cyclic. We show that in this case the outer automorphism group is virtually built from the outer automorphisms of the vertex groups (fixing some elements), the outer automorphisms of some associated generalised Baumslag-Solitar groups, and generalised twists - partial conjugations by elements in the centraliser of some elliptic elements in the group. This is joint work with D. Ascari and M. Casals-Ruiz.

4:00-5:00 From curve graphs to fine curve graphs, and back

Federica Fanoni (CNRS)

The fine curve graph has been recently introduced by Bowden, Hensel and Webb to study the homeomorphism group of a surface. I will talk about joint work with Sebastian Hensel where we try to understand to which extent the boundary of the fine curve graph of a surface can be understood via the curve graphs of the surface punctured at finitely many points. If time permits, I will also discuss how fine curve graph techniques can be used to construct a parabolic isometry of the nonseparating curve graph of an infinite-type surface of genus one.

Reimbursements

UPDATE: There is travel money available, prioritising speakers, PhD students, and ECRs. DO NOT FILL OUT ANY FORMS! Just send me an email at l.louder AT ucl.ac.uk and I will set things in motion.

We are on less of a shoestring budget than we were, but still try to minimize your travel costs!