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Oxford Graduate Texts in Mathematics #04: Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces


Oxford Graduate Texts in Mathematics #04: Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces Cover


Synopses & Reviews

Publisher Comments:

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 Schrodinger 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.

About the Author

Nigel Hitchin is Savilian Professor of Geometry at the University of Oxford

Graeme Segal is Emeritus Fellow of All Souls College, University of Oxford

Richard Ward is Professor in the Department of Mathematical Sciences, Durham University

Table of Contents

1. Introduction, Nigel Hitchin

2. Riemann surfaces and integrable systems, Nigel Hitchin

3. Integrable systems and inverse scattering, Graeme Segal

4. Integrable systems and twistors, Richard Ward


Product Details

Hitchin, N. J.
Clarendon Press
Segal, G. B.
Ward, R. S.
Mathematics | Pure Mathematics
Publication Date:
6.1 x 9.1 x 0.4 in 0.569 lb

Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Topology

Oxford Graduate Texts in Mathematics #04: Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces New Trade Paper
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Product details 148 pages Clarendon Press - English 9780199676774 Reviews:
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