Twistors, Loop Groups, and Riemann Surfaces
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Integrable Systems by N. J. Hitchin
Book DescriptionThis 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.
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Book DetailsISBN: 9780198504214
(241mm x 159mm x 13mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 18-Mar-1999
Country of Publication: United Kingdom
Books By Author N. J. Hitchin
Integrable Systems, Paperback (March 2013)
Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.
Surveys in Geometry and Number Theory, Paperback (January 2007)
A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.
Methods in Banach Space Theory, Paperback (November 2006)
A comprehensive overview of modern Banach space theory.
Lectures on the Ricci Flow, Paperback (October 2006)» View all books by N. J. Hitchin
An introduction to Ricci flow suitable for graduate students and research mathematicians.
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