Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces

(Author) (Author)
& 1 more
Usually delivers within 2 weeks.


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 Schroedinger 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.

Product Details

Oxford University Press
Publish Date
BIC Categories:

Earn By Promoting Books

Earn money by sharing your favourite books through our Affiliate programme.

Become an Affiliate
We use cookies and similar methods to recognize visitors and remember their preferences. We also use them to help detect unauthorized access or activity that violate our terms of service, as well as to analyze site traffic and performance for our own site improvement efforts. To learn more about these methods, including how to disable them view our Cookie Policy.