Title Integrable systems : twistors, loop groups, and Riemann surfaces : based on lectures given at a conference on integrable systems organized by N.M.J. Woodhouse and held at the Mathematical Institute, University of Oxford, in September 1997 / N.J. Hitchin, Savilian, professor of Geometry, University of Oxford, G.B. Segal, Lowndean, professor of Astronomy and Geometry, University of Cambridge, R.S. Ward, professor of Mathematics, University of Durham.

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Oxford : Clarendon Press, 2013.

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Online eBook via EBSCO. Access restricted to current Rider University students, faculty, and staff.
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Description	1 online resource.
Physical Medium	polychrome
Description	text file
Series	Oxford graduate texts in mathematics ; 4
	Oxford graduate texts in mathematics ; 4.
Bibliography	Includes bibliographical references.
Contents	Cover; Contents; List of contributors; 1 Introduction; Bibliography; 2 Riemann surfaces and integrable systems; 1 Riemann surfaces; 2 Line bundles and sheaves; 3 Vector bundles; 4 Direct images of line bundles; 5 Matrix polynomials and Lax pairs; 6 Completely integrable Hamiltonian systems; Bibliography; 3 Integrable systems and inverse scattering; 1 Solitons and the KdV equation; 2 Classical dynamical systems and integrability; 3 Some classical integrable systems; 4 Formal pseudo-differential operators; 5 Scattering theory; 6 The non-linear Schrodinger equation and its scattering.
	7 Families of flat connections and harmonic maps8 The KdV equation as an Euler equation; 9 Determinants and holonomy; 10 Local conservation laws; 11 The classical moment problem; 12 Inverse scattering; 13 Loop groups and the restricted Grassmannian; 14 Integrable systems and the restricted Grassmannian; 15 Algebraic curves and the Grassmannian; Bibliography; 4 Integrable Systems and Twisters; 1 General comments on integrable systems; 2 Some elementary geometry; 3 First example: self-dual Yang-Mills; 4 Twistor space and holomorphic vector bundles.
	5 Yang-Mills-Higgs solitons and minitwistor space6 Generalizations; Bibliography; Index; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; R; S; T; V; W; Y; Z.
Summary	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 werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu.
Local Note	eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject	Hamiltonian systems.
	Hamiltonian systems.
	Twistor theory.
	Twistor theory.
	Loops (Group theory)
	Loops (Group theory)
	Riemann surfaces.
	Riemann surfaces.
Genre/Form	Electronic books.
Added Author	Segal, Graeme.
	Ward, R. S. (Richard Samuel), 1951-
Other Form:	Print version: Hitchin, N.J. (Nigel J.), 1946- Integrable systems. Oxford : Clarendon Press, 2013 9780199676774 (DLC) 2013431016 (OCoLC)853436567
ISBN	9780191664458 (electronic book)
	0191664456 (electronic book)
	9780199676774
	0199676771

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