After doing all my degrees at the University of Cambridge I held postdoctoral positions in London, Zurich, Barcelona and Bonn, followed by permanent positions at the Ohio State University and at the University of Southampton. My research is in Geometric Group Theory and related areas including group cohomology and classifying spaces for families of subgroups. I see my research as driven by examples rather than by setting up theories.
- Geometric Group Theory
- Cohomology of Groups
- Classifying Spaces for Families of Subgroups
- Bestvina-Brady groups and generalizations of them
- CAT(0) Groups
Constructing interesting groups via graphical small cancellation
Residual finiteness of generalized Bestvina-Brady groups
Groups with surprising properties acting geometrically on the product of a tree and Euclidean space
Classifying spaces for families
I have been working on these topics with PhD students Tom Brown, Vlad Vankov, Sam Hughes and Kevin Li (Kevin jointly supervised with Nansen Petrosyan).
In recent years I have taught Representation Theory and Number Theory. I have also taught Group Theory, Algebraic Topology, Rings and Fields and Calculus, as well as supervising BSc/MMath projects on various topics.
Professor of Pure Mathematics, University of Southampton 2011-now
Professor of Mathematics The Ohio State University 2006-11
Associate Professor The Ohio State University 2004-06
Reader, University of Southampton 2002-04
Lecturer, University of Southampton 1997-2002
Postdoctoral Fellow, MPI Bonn 1995
Postdoctoral Fellow, CRM, Barcelona 1993-94
Postdoctoral Fellow, ETH Zurich 1992-93
SERC Postdoctoral Fellow, QMW London 1990-92
PhD and Undergraduate student University of Cambridge 1983-90