Dietmar Salamon

N. J. Hitchin

This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990.

Symplectic Geometry

J. W. P. Hirschfeld

Reader in Mathematics J W P Hirschfeld

The British Combinatorial Conference is held every two years and is now a key event for mathematicians worldwide, working in combinatorics. This volume is published on the occasion of the 18th meeting, which was held 1st-6th July 2001 at the University of Sussex. The papers contained here are surveys contributed by the invited speakers, and are thus of a quality befitting the event. There is also a tribute to Crispin Nash-Williams, past chairman of the British Combinatorial Committee. The diversity of the subjects covered means that this will be a valuable reference for researchers in combinatorics. However, graduate students will also find much here that could be of use for stimulating future research.

Surveys in Combinatorics, 2001

R. S. Ward

G. B. Segal

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do we recognize an integrable system? His own contribution then develops connections with algebraic geometry, and includes an introduction to Riemann surfaces, sheaves, and line bundles. Graeme Segal takes the Kortewegde Vries and nonlinear Schrödinger equations as central examples, and explores the mathematical structures underlying the inverse scattering transform. He explains the roles of loop groups, the Grassmannian, and algebraic curves. In the final part of the book, Richard Ward explores the connection between integrability and the self-dual Yang-Mills equations, and describes the correspondence between solutions to integrable equations and holomorphic vector bundles over twistor space.

Twistors, Loop Groups, and Riemann Surfaces

Integrable Systems

Savilian Professor of Geometry N J Hitchin

P. E. Newstead

W. M. Oxbury

This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.

N. J. Hitchin

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