## Status:

Professor of Mathematics

Fellow of Wadham College

## Research groups:

## Address

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

## Recent Publications:

Duality for the general isomonodromy problem.

Journal of Geometry and Physics
issue 4
volume 57
page 1147-1170
(March 2007)

Painleve VI, hypergeometric hierarchies and Ward ansatze

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
issue 39
volume 39
page 12265-12269
(29 September 2006)
Full text available

Two twistor descriptions of the isomonodromy problem

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
issue 15
volume 39
page 4087-4093
(14 April 2006)
Full text available

The geometry of dual isomonodromic deformations

Journal of Geometry and Physics
issue 1
volume 52
page 44-56
(September 2004)

Tau-functions, twistor theory, and quantum field theory

Communications in Mathematical Physics
issue 3
volume 230
page 389-420
(November 2002)

## Research interests:

**Twistors and the isomonodromy deformation problem**. Isomonodromic deformations of systems of ordinary differential equations play a central part in our understanding of the complex geometry of integrable systems, and also reveal connections, through the theory of Frobenius manifolds, between twistor theory and quantum field theory.

Twistor theory was developed by Roger Penrose. His original aim was to find a route to the quantization of gravity. The underlying mathematical ideas have proved to have rich applications in geometry and in the analysis of integrable systems.

**Geometric quantization** is a general framework for constructing quantum systems from their classical counterparts, starting from the symplectic geometry of the classical phase space. The theory is described in Geometric quantization (second edition, Oxford University Press, 1992).

**General relativity**

## Preferred address:

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford OX2 6GG, UK