Integrable Systems. Twistors, Loop Groups, and Riemann Surfaces.

Hitchin, N J, G B Segal and R S Ward:

ISBN 10: 0198504217 / ISBN 13: 9780198504214

Published by Oxford University Press, 1999

About this Item

Series: Oxford Graduate Texts in Mathematics. viii 136p hardback in sturdy red and green cover, very look condition, little to no wear, tight binding, very clean and neat pages, an excellent copy with little sign of use Language: English Weight (g): 310.

Seller Inventory # 233146

Bibliographic Details

• Title: Integrable Systems. Twistors, Loop Groups, and Riemann Surfaces.
• Publisher: Oxford University Press
• Publication Date: 1999
• Language: English
• ISBN 10: 0198504217
• ISBN 13: 9780198504214
• Binding: Hardback
• Edition: 1st Edition
• Condition: Very Good
• Weight: 310 grams
• Seller catalogs:
  • Mathematics

About this title

Synopsis

This textbook for graduate students introduces integrable systems through the study of Riemann surfaces, loop groups, and twistors. The introduction by Nigel Hitchin addresses the meaning of integrability, discussing in particular how to recognize an integrable system. He then develops connections between integrable systems and algebraic geometry and introduces Riemann surfaces, sheaves, and line bundles. In the next part, Graeme Segal takes the Korteweg-de Vries and nonlinear Schrödinger equations as central examples and discusses the mathematical structures underlying the inverse scattering transform. He also explains loop groups, the Grassmannian, and algebraic curves. In the final part of the book, Richard Ward explores the connection between integrability and self-dual Yang-Mills equations and then describes the correspondence between solutions to integrable equations and holomorphic vector bundles over twistor space.

About the Author

N. J. Hitchin is Savilian Professor of Geometry, University of Oxford.