Status:
ORCID iD:
https://orcid.org/0000-0002-7669-3304
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Books:
An introduction to intersection homology theory
ISBN-13: 9781584881841
(2006)
Geometric invariant theory
ISBN-10: 3-540-56963-4
(1994)
Complex algebraic curves
ISBN-13: 9780521412513
(1992)
Cohomology of quotients in symplectic and algebraic geometry
ISBN-13: 9780691083704
(1984)
Highlighted Publications:
Stratifying quotient stacks and moduli stacks
Abelsymposium 2017: Geometry of Moduli
volume 14
page 1-33
(24 November 2018)
Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics.
Bull. Lond. Math. Soc.
volume 40 (2008)
page 533-567
(August 2008)
Towards non-reductive geometric invariant theory
Pure and Applied Mathematics Quarterly
issue 1
volume 3
page 61-105
(2007)
Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface
Ann. of Math. (2)
issue 1
volume 148
page 109-196
(1998)
Localization and the quantization conjecture
Topology
issue 3
volume 36
page 647-693
(1997)
The cohomology rings of moduli spaces of bundles over Riemann surfaces
J. Amer. Math. Soc.
issue 4
volume 5
page 853-906
(1992)
Rational intersection cohomology of quotient varieties
Invent. Math.
issue 3
volume 86
page 471-505
(1986)
Partial desingularisations of quotients of nonsingular varieties and their Betti numbers
Ann. of Math. (2)
issue 1
volume 122
page 45-85
(1985)
Convexity properties of the moment mapping. III.
Invent. Math.
issue 3
volume 77
page 547-552
(1984)
Recent Publications:
Morse theory without nondegeneracy
Quarterly Journal of Mathematics
(17 December 2020)
Symplectic quotients of unstable Morse strata for normsquares of moment maps
Communications in Analysis and Geometry
issue 4
volume 28
page 837-870
(1 October 2020)
Constructing quotients of algebraic varieties by linear algebraic group actions
Handbook of Group Actions, Volume IV
page 341-446
(16 November 2018)
Variation of non-reductive geometric invariant theory
Journal of Differential Geometry 2017 Conference
(13 September 2018)
Research interests:
Algebraic and symplectic geometry
Prizes, awards, and scholarships:
- London Mathematical Society Whitehead Prize, 1989
- Fellow of the Royal Society, 2001
- President, London Mathematical Society, 2003-2005
- EPSRC Senior Research Fellowship, 2005-2010
- London Mathematical Society Senior Whitehead Prize, 2013
- DBE, 2014