Integrable Systems. Twistors, Loop Groups, And Riemann Surfaces - Couverture rigide

Hitchin, N-J

 
9780198504214: Integrable Systems. Twistors, Loop Groups, And Riemann Surfaces
Couverture rigide
ISBN 10 : 0198504217 ISBN 13 : 9780198504214
Editeur : Oxford University Press, 1999

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

"the subject of the book is fascinating and written versions of the lecture series are nicley presented and preserve well the informal spirit of the lectures. This is a very useful book for graduate students and for mathematicians (or physicists) from other fields interested in the topic' EMS

"The lecturers cover an enormous amount of material, ranging from algeraic geometry and the theory of Riemann surfaces to loop groups, connections, Yang-Mills equations and twister theory. However despite this wide range, the book is surprisingly self-contained and readable" Bulletin of the London Mathematical Society"

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Oxford University Press
Date d'édition
1999
Langue
anglais
ISBN 10 
0198504217
ISBN 13 
9780198504214
Reliure
Relié
Numéro d'édition
1
Nombre de pages
148
Coordonnées du fabricant
non disponible
Personne responsable
Ufficio Anagrafiche Messaggerie
ufficio.anagrafiche@meli.it

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