This week, the ICMAT is hosting a school on mapping class groups, surface subgroups, bundles, and group extensions. Image: Íñigo de Amescua/ICMAT

From 5 to 9 May, ICMAT is holding the Advanced School on Mapping Class Groups, Surface Subgroups, Bundles, and Group Extensions. In this school, 15 specialists in the field of geometric group theory – which studies groups, an algebraic concept capturing the notion of symmetry, from a geometric perspective – will introduce, for PhD students, postdocs, and other interested participants, some of the most active topics in the area. Specifically, on mapping class groups, surface subgroups, bundles, and group extensions.

The programme focuses on a series of lectures by Autumn Kent (University of Wisconsin, USA) and Chris Leininger (Rice University, USA), based on their recent work on constructing purely pseudo-Anosov surface subgroups of mapping class groups.

To facilitate understanding of these recent developments, the school includes introductory talks on related topics by invited speakers, as well as other research talks.

This school, organised by Martin Bridson (University of Oxford, UK), Andrei Jaikin (ICMAT), and Alan Reid (Rice University, USA), is one of the first activities of the Bridson-Reid Laboratory, launched in 2024 as part of the fourth edition of the ICMAT Severo Ochoa Excellence Programme’s Distinguished Laboratories and Professors initiative.

Bridson-Reid Laboratory

The Bridson-Reid Laboratory focuses on geometric group theory, which uses tools and concepts from geometry and topology to understand the structure and properties of groups. It aims to contribute to solving fundamental mathematical problems in geometric group theory, hyperbolic geometry, and the topology of three-dimensional manifolds.

The research group is co-led by Alan Reid, currently Professor at Rice University (USA), and Martin Bridson, Professor at the University of Oxford (UK), who is also Director of the Clay Mathematics Institute, an institution dedicated to funding and promoting mathematics – among its initiatives is the Millennium Problems list, whose solutions are awarded one million dollars. The former has achieved highly influential results in geometric group theory, hyperbolic geometry, and the topology of three-dimensional manifolds. The latter specialises in low-dimensional topology, geometric group theory, and non-positively curved spaces, and has received several distinctions, including the LMS Whitehead Prize (1999), the Royal Society Wolfson Research Merit Award (2012), and the AMS Steele Prize (2020).

The laboratory is coordinated by Andrei Jaikin, Professor at the Universidad Autónoma de Madrid and member of ICMAT.