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- Reader in Mathematics
- Dept of Mathematics
- Faculty of Maths & Physical Sciences
I was awarded an EPSRC Career Acceleration Fellowship, which ran from 1 September 2009 until 31 August 2014. From the start of my fellowship until my appointment at UCL, I was a member of the Geometry group at Imperial College London. I was also awarded an EPSRC Mathematical Sciences Small Grant (with Haskins as Co-I), LMS Scheme 1 and Scheme 3 Grants and recently an EPSRC Standard Grant (as PI) and funding for an LMS-CMI Research School (with Haskins and Salamon as co-organisers). I am currently the LMS Rep for UCL.
During the academic years 05-07 and 08-09 I was a Junior Research Fellow at University College, Oxford. I was awarded an NSF Mathematical Sciences Postdoctoral Research Fellowship and spent the academic year 07-08 at the Mathematical Sciences Research Institute, Berkeley, working with Robert Bryant.
I studied for my DPhil at Oxford from 02-05 under the supervision of Dominic Joyce. During this time I was first at New College before moving to Christ Church upon the award of a Senior Scholarship. I had previously been at St Edmund Hall, Oxford, for my undergraduate degree in Mathematics.
I work on differential geometry, with a particular focus on manifolds with special holonomy, their calibrated submanifolds, and related geometries. I am also interested in geometric flows, including Lagrangian mean curvature flow and the Laplacian flow, and instantons. 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 because of their special nature, their connections with Einstein metrics and gauge theory, and also their relations with 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 have designed and continue to teach a 4th year course on Riemannian Geometry. I have designed and taught a new 2nd year course on Geometry and Groups. This year I taught Calculus and Linear Algebra for 1st year non-mathematics undergraduates, and I have previously given problem classes for Analysis 1 for 1st year maths undergraduates. I will be teaching an extended course for PhD students on Calibrated Geometry and Geometric Flows for the London Taught Course Centre.
I have supervised four 1st year PhD projects, two 4th year projects, a 2nd year project, and supervised three completed PhD students. I currently supervise three PhD students and five first year PhD project students.
|2006||DPhil||Doctor of Philosophy – Mathematics||University of Oxford|
|2002||MMath||Master of Mathematics – Mathematics||University of Oxford|