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Integrable Systems, Topology, and Physics
Edited by: Martin Guest, Tokyo Metropolitan University, Japan, Reiko Miyaoka, Sophia University, Tokyo, Japan, and Yoshihiro Ohnita, Tokyo Metropolitan University, Japan
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Contemporary Mathematics
2002; 324 pp; softcover
Volume: 309
ISBN-10: 0-8218-2939-4
ISBN-13: 978-0-8218-2939-4
List Price: US$98
Member Price: US$78.40
Order Code: CONM/309
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Ideas and techniques from the theory of integrable systems are playing an increasingly important role in geometry. Thanks to the development of tools from Lie theory, algebraic geometry, symplectic geometry, and topology, classical problems are investigated more systematically. New problems are also arising in mathematical physics. A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles.

This volume focuses on topology and physics. The role of zero curvature equations outside of the traditional context of differential geometry has been recognized relatively recently, but it has been an extraordinarily productive one, and most of the articles in this volume make some reference to it. Symplectic geometry, Floer homology, twistor theory, quantum cohomology, and the structure of special equations of mathematical physics, such as the Toda field equations--all of these areas have gained from the integrable systems point of view and contributed to it.

Many of the articles in this volume are written by prominent researchers and will serve as introductions to the topics. It is intended for graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics.

The first volume from this conference, also available from the AMS, is Differential Geometry and Integrable Systems, Volume 308 in the Contemporary Mathematics series. The forthcoming third volume will be published by the Mathematical Society of Japan and will be available outside of Japan from the AMS in the Advanced Studies in Pure Mathematics series.

Readership

Graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics.

Table of Contents

  • L. Casian and Y. Kodama -- Twisted Tomei manifolds and the Toda lattices
  • J.-H. Chang -- Quantization of Benney hierarchies
  • K. Fukaya -- Floer homology for families-A progress report
  • R. Goto -- Rozansky-Witten invariants of log symplectic manifolds
  • M. A. Guest -- An update on harmonic maps of finite uniton number, via the zero curvature equation
  • R. Inoue -- The lattice Toda field theory for simple Lie algebras
  • H. Konno -- On the cohomology ring of the hyperKähler analogue of the polygon spaces
  • A.-L. Mare -- On the theorem of Kim concerning \(QH^*(G/B)\)
  • Y. Nagatomo -- Geometry of the twistor equation and its applications
  • A. Nakayashiki -- On the cohomology of theta divisors of hyperelliptic Jacobians
  • Y. Ohyama -- Isomonodromy deformations and twistor theory
  • K. Ono -- Simple singularities and symplectic fillings
  • T. Otofuji -- Quantum cohomology of infinite dimensional flag manifolds
  • S. Saito, N. Suzuki, and H. Yamaguchi -- Discrete conjugate nets of strings
  • B. A. Shipman -- Nongeneric flows in the full Kostant-Toda lattice
  • I. A. B. Strachan -- Frobenius manifolds and bi-Hamiltonian structures on discriminant hypersurfaces
  • T. Taniguchi -- Periodicity conditions for harmonic maps associated to spectral data
  • Y. Terashima -- Higher dimensional parallel transports for Deligne cocycles
  • H.-Y. Wang -- Geometric nonlinear Schrödinger equations
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