## Geometric Group Theory

26 Feb 2016, by Events inOrganisers: Talia Fernós, Graham Niblo, Piotr Nowak and John Britnell

Description

Geometric group theory has become a central area of research in Pure Mathematics with research groups across Europe and the Americas. The ideas started in 1968 with Mostow’s rigidity theorem (in the co-compact case) and the work of Wolf and Milnor on growth of groups. The impetus came in 1981 with Gromov’s proof of his polynomial growth theorem, in which virtually nilpotent groups were characterized in terms of their large-scale geometry, namely polynomial volume growth. Since it’s inception, geometric group theory has developed into a separate branch of geometry with deep links to other parts of mathematics. In the last 15 years it has seen a fruitful interaction with non-commutative geometry and index theory. The use of large-scale geometric methods led to spectacular progress in the Baum-Connes-type conjectures. This in particular implies the Novikov conjecture for many new classes of groups and has applications to the positive scalar curvature problem, the Gromov-Lawson-Rosenberg conjecture and Gromov’s zero-in-the-spectrum conjecture.

For this workshop we plan a particular emphasis on the interaction between geometric group theory and non-commutative geometry, in particular focusing on approximation properties including amenability, the Haagerup property, property A (group C*-exactness) and their connections to homology and cohomology theories of groups.

Main Speakers

Arthur Bartels (Universität Münster)

Jacek Brodzki (University of Southampton)

Martin Bridson (University of Oxford)

Cornelia Drutu (University of Oxford)

Steve Ferry (Rutgers University)

Erik Guentner (University of Hawaii)

Nigel Higson (Pennsylvania State University)

John Roe (Pennsylvania State University)

Alain Valette (Université de Neuchâtel)

Guoliang Yu (Vanderbilt University)

Andrzej Żuk (Université Paris 7)