**Contemporary Mathematics**

Volume: 309;
2002;
324 pp;
Softcover

MSC: Primary 35; 37; 53; 58; 70;

Print ISBN: 978-0-8218-2939-4

Product Code: CONM/309

List Price: $103.00

Individual Member Price: $82.40

**Electronic ISBN: 978-0-8218-7899-6
Product Code: CONM/309.E**

List Price: $103.00

Individual Member Price: $82.40

# Integrable Systems, Topology, and Physics

Share this page *Edited by *
*Martin Guest; Reiko Miyaoka; Yoshihiro Ohnita*

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

#### Table of Contents

# Table of Contents

## Integrable Systems, Topology, and Physics

- Contents v6 free
- Twisted Tomei manifolds and the Toda lattices 118 free
- Quantization of Benney hierarchies 2138
- Floer homology for families — a progress report 3350
- Rozansky-Witten invariants of log symplectic manifolds 6986
- An update on harmonic maps of finite uniton number, via the zero curvature equation 85102
- The lattice Toda field theory for simple Lie algebras 115132
- On the cohomology ring of the hyperKähler analogue of the polygon spaces 129146
- On the theorem of Kim concerning QH*(G/B) 151168
- Geometry of the twistor equation and its applications 165182
- On the cohomology of theta divisors of hyperelliptic Jacobians 177194
- Isomonodromy deformations and twistor theory 185202
- Simple singularities and symplectic fillings 195212
- Quantum cohomology of infinite dimensional flag manifolds 199216
- Discrete conjugate nets of strings 211228
- Nongeneric flows in the full Kostant-Toda lattice 219236
- Frobenius manifolds and bi-Hamiltonian structures on discriminant hypersurfaces 251268
- Periodicity conditions for harmonic maps associated to spectral data 267284
- Higher dimensional parallel transports for Deligne cocycles 291308
- Geometric nonlinear Schrödinger equations 313330

#### Readership

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