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- Reader in Mathematics
- Dept of Mathematics
- Faculty of Maths & Physical Sciences

I am a Reader in Mathematics at University College London, effective from 1 October 2014. I was appointed as a Lecturer in Pure Mathematics at UCL on 1 April 2011.

I currently am Co-PI on a Leverhulme Research Project Grant (with Felix Schulze, UCL) and PI on an HIMR Focused Research Grant. 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 have also been awarded an EPSRC Mathematical Sciences Small Grant (with Haskins as Co-I), LMS Scheme 1 and Scheme 3 Grants, 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, member of the LMS and AMS and member of the EPSRC Peer Review College.

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. Last year I taught Calculus and Linear Algebra for a large class of 1st year non-mathematics undergraduates, and I have previously given problem classes for Analysis 1 for 1st year maths undergraduates. I also taught an extended course for PhD students on Calibrated Geometry and Geometric Flows for the London Taught Course Centre, and give a Topics in Geometry lecture each year to PhD students at the London School for Geometry and Number Theory (LSGNT).

I have supervised nine 1st year PhD projects (as part of the LSGNT programme), three 4th year projects (including one from Physics), one visiting Masters student, two 2nd year projects, and supervised three completed PhD students. I currently supervise six PhD students.

01-OCT-2014 | Reader in Mathematics | Mathematics | University College London, United Kingdom |

01-APR-2011 – 30-SEP-2014 | Lecturer in Mathematics & EPSRC Career Acceleration Fellow | Mathematics | University College London, United Kingdom |

01-SEP-2009 – 31-MAR-2011 | EPSRC Career Acceleration Fellow | Mathematics | Imperial College, London, United Kingdom |

01-SEP-2008 – 31-AUG-2009 | Lecturer in Mathematics | St Edmund Hall, University of Oxford, United Kingdom | |

01-SEP-2007 – 31-AUG-2008 | NSF Mathematical Sciences Postdoctoral Research Fellow | Mathematical Sciences Research Institute, Berkeley, United States | |

01-SEP-2005 – 31-AUG-2009 | Junior Research Fellow in Science | University College, University of Oxford, United Kingdom | |

01-SEP-2002 – 31-AUG-2007 | Lecturer in Mathematics | St Edmund Hall, University of Oxford, United Kingdom |

2006 | DPhil | Doctor of Philosophy – Mathematics | University of Oxford |

2002 | MMath | Master of Mathematics – Mathematics | University of Oxford |