Integrable Systems / Comparative Pathobiology - Studies in the Postmodern Theory of Education (PDF)
Twistors, Loop Groups, and Riemann Surfaces
(Sprache: Englisch)
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...
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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.
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.
Autoren-Porträt von N. J. Hitchin, G. B. Segal, R. S. Ward
Nigel Hitchin is Savilian Professor of Geometry at the University of OxfordGraeme Segal is Emeritus Fellow of All Souls College, University of Oxford
Richard Ward is Professor in the Department of Mathematical Sciences, Durham University
Bibliographische Angaben
- Autoren: N. J. Hitchin , G. B. Segal , R. S. Ward
- 2013, Englisch
- Verlag: Oxford University Press
- ISBN-10: 0191664456
- ISBN-13: 9780191664458
- Erscheinungsdatum: 14.03.2013
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- Grösse: 4.95 MB
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Englisch
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