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Integrable systems, geometry, and topology

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 the...

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Autor principal: Terng, Chuu-Lian
Lenguaje:eng
Publicado: American Mathematical Society 2006
Materias:
Acceso en línea:http://cds.cern.ch/record/2279766
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author Terng, Chuu-Lian
author_facet Terng, Chuu-Lian
author_sort Terng, Chuu-Lian
collection CERN
description 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.
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spelling cern-22797662021-04-21T19:05:40Zhttp://cds.cern.ch/record/2279766engTerng, Chuu-LianIntegrable systems, geometry, and topologyMathematical Physics and MathematicsThe 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.American Mathematical Societyoai:cds.cern.ch:22797662006
spellingShingle Mathematical Physics and Mathematics
Terng, Chuu-Lian
Integrable systems, geometry, and topology
title Integrable systems, geometry, and topology
title_full Integrable systems, geometry, and topology
title_fullStr Integrable systems, geometry, and topology
title_full_unstemmed Integrable systems, geometry, and topology
title_short Integrable systems, geometry, and topology
title_sort integrable systems, geometry, and topology
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2279766
work_keys_str_mv AT terngchuulian integrablesystemsgeometryandtopology