AMS/IP Studies in Advanced Mathematics
Volume: 36; 2006; 256 pp; Softcover
MSC: Primary 14; 35; 37; 53; 58;
Print ISBN: 978-0-8218-4048-1
Product Code: AMSIP/36
List Price: $65.00
Individual Member Price: $52.00
Integrable Systems, Geometry, and TopologyShare this page
Edited by Chuu-Lian Terng
A co-publication of the AMS and International Press of Boston, Inc.
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.
Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
Table of Contents
Table of Contents
Integrable Systems, Geometry, and Topology
Research mathematicians interested in integrable systems.