I work on Differential Geometry, with a particular focus on calibrated submanifolds of 7 and 8-dimensional Riemannian manifolds with exceptional holonomy, and related geometries. I am also interested in Lagrangian mean curvature flow. I mainly use methods from Geometric Analysis and Exterior Differential Systems, which have applications throughout Geometry and other areas in mathematics. The geometries I study are important from the mathematical point of view both because of their special nature, since they can only occur in certain dimensions and are connected with gauge theory, and also because they are related to the familiar and well-studied theories of minimal submanifolds and complex geometry. Moreover, the objects I investigate are of potential importance in high-energy theoretical physics, appearing in a number of papers on String Theory and M-Theory. I am an EPSRC Career Acceleration Fellow and Lecturer in Pure Mathematics at University College London. I have recently moved from Imperial College London and I spent the academic year 07-08 at MSRI, Berkeley, working with Robert Bryant. My DPhil supervisor was Dominic Joyce. I am a co-organiser of the joint King's/UCL Geometry Seminar. | ||||||||||||||||||
