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Integrable Systems, Geometry, and Topology
 
Edited by: Chuu-Lian Terng University of California, Irvine, Irvine, CA
A co-publication of the AMS and International Press of Boston
Front Cover for Integrable Systems, Geometry, and Topology
Available Formats:
Softcover ISBN: 978-0-8218-4048-1
Product Code: AMSIP/36
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
Electronic ISBN: 978-1-4704-3825-8
Product Code: AMSIP/36.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $103.50
MAA Member Price: $93.15
AMS Member Price: $82.80
Front Cover for Integrable Systems, Geometry, and Topology
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  • Front Cover for Integrable Systems, Geometry, and Topology
  • Back Cover for Integrable Systems, Geometry, and Topology
Integrable Systems, Geometry, and Topology
Edited by: Chuu-Lian Terng University of California, Irvine, Irvine, CA
A co-publication of the AMS and International Press of Boston
Available Formats:
Softcover ISBN:  978-0-8218-4048-1
Product Code:  AMSIP/36
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
Electronic ISBN:  978-1-4704-3825-8
Product Code:  AMSIP/36.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $103.50
MAA Member Price: $93.15
AMS Member Price: $82.80
  • Book Details
     
     
    AMS/IP Studies in Advanced Mathematics
    Volume: 362006; 256 pp
    MSC: Primary 14; 35; 37; 53; 58;

    The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems.

    The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model.

    The book provides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians.

    Readership

    Research mathematicians interested in integrable systems.

  • Table of Contents
     
     
    • Chapters
    • Isothermic surfaces: Conformal geometry, Clifford algebras and integrable systems
    • Introduction to homological geometry: part I
    • Introduction to homological geometry: part II
    • Isoparametric submanifolds and a Chevalley-type restriction theorem
    • Gauge-Theoretic approach to harmonic maps and subspaces in moduli spaces
    • Schrödinger flows on Grassmannians
  • Additional Material
     
     
  • Request Review Copy
Volume: 362006; 256 pp
MSC: Primary 14; 35; 37; 53; 58;

The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems.

The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model.

The book provides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians.

Readership

Research mathematicians interested in integrable systems.

  • Chapters
  • Isothermic surfaces: Conformal geometry, Clifford algebras and integrable systems
  • Introduction to homological geometry: part I
  • Introduction to homological geometry: part II
  • Isoparametric submanifolds and a Chevalley-type restriction theorem
  • Gauge-Theoretic approach to harmonic maps and subspaces in moduli spaces
  • Schrödinger flows on Grassmannians
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