Awards
- Fröhlich prize, London Mathematical Society, 2022
- President’s Award for Excellence in Education, Imperial College London, 2020
- Royal Society research professorship, , 2020
- Member, Academia Europaea, , 2019
- Fellow of the American Mathematical Society, , 2018
- Excellence in Teaching Prize, Faculty of Natural Sciences, 2015
- Fellow of the Royal Society, , 2015
- Invited speaker, International Congress of Mathematicians, 2010
- Wolfson Merit Award, Royal Society, 2010
- Philip Leverhulme Prize, 2004
- Whitehead Prize, London Mathematical Society, 2004
External Positions
- External examiner, University of Oxford, University of Oxford, 2012 - 2016
- Scientific Steering Committee, Isaac Newton Institute for Mathematical Sciences, Cambridge
Membership of Professional Bodies
- Member, European Algebraic Geometry Research Training Network (EAGER)
- Member, European Differential Geometry Endeavour (EDGE)
- Member, London Mathematical Society
Fellowships
- Taussky-Todd Moore Distinguished Scholar, Caltech, 2012 - 2012
- Research Professor, MSRI, Berkeley, 2009 - 2009
- Visiting Professor, UBC, Vancouver, 2008 - 2008
- Visiting Scholar, Columbia University, New York, 2007 - 2007
- Visiting CNRS fellow, Jussieu, Paris, 2005 - 2005
- Visiting fellow, Newton Institute, Cambridge, 2002 - 2002
- Visiting fellow, M.I.T., 2001 - 2001
- Visiting research fellow, Harvard University, 1999 - 2000
- Member, Institute for Advanced Study, Princeton, 1997 - 1998
Editorial Boards
- Selecta Mathematica, Member of editorial board
- Forum of mathematics, Pi and Sigma, Editorial board
- Online Encyclopaedia of Mathematics, Editor
- Geometry & Topology, Member of editorial board
- Algebraic geometry, Editorial board