Martin Bridson-Alan Reid Laboratory

Martin Bridson (University of Oxford, UK; Clay Mathematics Institute, USA)

Martin Bridson is the Whitehead Professor of Pure Mathematics at the University of Oxford (UK) and the Director of the Clay Mathematics Institute, which supports the advancement of mathematics through funding and various initiatives. Bridson specializes in low-dimensional topology, geometric group theory, and spaces of non-positive curvature. His numerous honors include the LMS Whitehead Prize (1999), the Wolfson Research Merit Award from the Royal Society (2012), and the Steele Prize for Mathematical Exposition from the American Mathematical Society (2020).

Alan Reid (Rice University, USA)

Alan Reid currently holds the Edgar Odell Lovett Chair of Mathematics at Rice University (USA). He is a Fellow of the American Mathematical Society (AMS) and a Corresponding Fellow of the Royal Society of Edinburgh. Reid’s research focuses on geometric group theory, hyperbolic geometry, and the topology of 3-manifolds, fields in which he has made highly influential contributions.

Research field

Geometric Group Theory.

Research project

We will focus on various aspects of geometric group theory. One of the topics this lab will address is profinite rigidity. Profinite rigidity refers to the property of a finitely generated, residually finite group being completely determined by its profinite completion. In other words, a finitely generated residually finite group G is profinitely rigid if, whenever a finitely generated residually finite group H has the same profinite completion as G, then H is isomorphic to G. Concretely, we are interested in obtaining results related to the Remeslennikov conjecture, which predicts that finitely generated free groups are profinitely rigid.

Members

Martin Bridson (University of Oxford, UK; Clay Mathematics Institute, USA) – chair
Alan Reid (Rice University, USA) – chair
Andrei Jaikin (ICMAT-UAM) – coordinator
Yago Antolín (ICMAT-UCM)
Javier Aramayona (ICMAT-CSIC)
Caterina Campagnolo (ICMAT-UAM)
Dominik Francouer (UAM)
Alejandra Garrido (UCM)
Marco Linton (ICMAT-CSIC)
Leo Margolis (ICMAT-UAM)