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

UCL 25 October 2024

Lecture Theatre G22, North - West Wing

Directions to the room. You cannot enter the building through the southernmost door. From the UCL Gower St entrance enter the main quad and proceed to your left, along the eastern side of the building labeled North-West Wing.

1:20-2:20 TITLE

Rémi Coulon (Dijon)

2:30-3:30 Long curves and random hyperbolic surfaces

James Farre (Leipzig)

We will fix some topological data, a pants decomposition, of a closed surface and build hyperbolic structures by gluing hyperbolic pairs of pants along their boundary. The set of all hyperbolic metrics with a pants decomposition having a given set of lengths defines an immersed torus in the moduli space of hyperbolic metrics—a "twist torus." Mirzakhani conjectured that as the lengths of the pants curves tend to infinity, that the corresponding twist tori equidistribute in the moduli space. We address Mirzakhani’s conjecture and explain how to import tools in Teichmüller dynamics on a moduli space of singular flat surfaces with cone points to dynamics on the moduli space of hyperbolic surfaces equipped with a measured geodesic lamination. This is joint work with Aaron Calderon.

3:30-4:00 TEA

4:00-5:00 Reconstructing CAT(0) cube complexes from boundary distances

Jane Tan (Oxford)

Given a quadrangulation of a disc, suppose we know all the pairwise distances (measured by the graph metric) between vertices on the boundary of the disc. Somewhat surprisingly, a result of Haslegrave states that this is enough information to recover the whole interior structure of the quadrangulation provided all internal vertex degrees are at least 4. In joint work with Haslegrave, Scott and Tamitegama, we tried to generalise this result to 3-dimensional cube complexes, which is how a group of combinatorialists accidentally delved into the world of CAT(0) cube complexes. In this talk, we’ll discuss the combinatorial motivations for this work, and discuss our result as well as that of Chalopin and Chepoi who have since further generalised our work.

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!