School of Mathematics, Statistics and Physics

Geometric Group Theory

Geometric Group Theory

Overview

An association between geometry and group theory can be traced back to Klein's crucial observation, in the late 19th century, that geometric constructions can be understood in terms of their symmetry groups.

It soon emerged that the reverse process could also be useful, for example early in the 20th century Dehn used techniques of topology to answer questions of logic arising in group theory. In the 1970s and 80s such ideas were unified and extended by Thurston, Cannon and particularly Gromov, who used the geometric properties of spaces on which groups act to study groups, and vice-versa. This interplay between geometry and group theory, which is the subject of geometric group theory, has been very fruitful and the theory has expanded rapidly in the last few decades.

Notable successes are applications in 3-manifold theory, complex dynamics, first order logic, the theory of formal languages, Riemannian geometry and representation theory.

Staff

The following members of staff from the School of Mathematics and Statistics are members of the Geometric Group Theory research group.

Dr Andrew Duncan
Reader in Algebra

Email:
Telephone: +44 (0) 191 208 8737

Professor Peter Jorgensen
Professor of Pure Mathematics

Email:
Telephone: +44 (0) 191 208 7288

Dr Oli King
Senior Lecturer in Pure Mathematics

Email:
Telephone: +44 (0) 191 208 7277

Professor Sarah Rees
Professor of Pure Mathematics

Email:
Telephone: +44 (0) 191 208 7236

Dr Alina Vdovina
Senior Lecturer in Pure Mathematics

Email:
Telephone: +44 (0) 191 208 7314