## 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:

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)

Graded linearisations

Modern Geometry — A celebration of the work of Simon Donaldson
volume 99
page 1-22
(5 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