Research Interests

My interests are in global problems in differential geometry, especially those where elliptic PDE plays a role. My most recent work has been in the area of extremal Kaehler metrics (including Kaehler metrics of constant scalar curvature) with collaborators Claudio Arezzo, Frank Pacard, and Yann Rollin. I have an on-going collaborative project with Joel Fine in this area.

I also have a long-term interest in non-abelian magnetic monopoles, both in euclidean and hyperbolic space, and have written several papers on the subject with Michael Murray. I have a major on-going project aimed at a refined understanding of the monopole moduli space and its hyperKaehler metric - an area where Roger Bielawski has made major contributions in recent years.

Research Groups

• Geometry and Topology
• Mathematical Physics

Current and Recent PhD Students

Ruth Hawksley (PhD 1999)

Tom Nye (PhD 2001)

Hugh Griffiths (started 2004)

Florian Pokorny (PhD 2011)

Recent Conference and Workshop Involvement

ICMS workshop on Extremal Kaehler metrics and stability, Edinburgh 2006, co-organized with Claude LeBrun (Stony Brook) and Richard Thomas (Imperial College London)

Biographical Statement

I studied Mathematics at Cambridge (England) 1979-1983 and then went to Oxford as a graduate student under the supervision of Roger (now Sir Roger) Penrose. I was then awarded a Junior Research Fellowship in Mathematics at Merton College, Oxford, before taking on the Darby Fellowship in Mathematics at Lincoln College. I came to Edinburgh in July 1994 following 7 months at Adelaide and 3 months at the Newton Institute, Cambridge.

I spent my sabbatical year 2003--4 visiting the Mathematics Department at MIT.