Integrable Systems, Topology, and Physics
About this Title
Martin Guest, Reiko Miyaoka and Yoshihiro Ohnita, Editors
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 topolgoy, 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 first 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.
Graduate students and researchers interested in integrable systems and their relations to differential geometry, topology, algebraic geometry, and physics.
Table of Contents
- Luis Casian and Yuji Kodama – Twisted Tomei manifolds and the Toda lattices [MR 1953350]
- Jen-Hsu Chang – Quantization of Benney hierarchies [MR 1953351]
- Kenji Fukaya – Floer homology for families—a progress report [MR 1953352]
- Ryushi Goto – Rozansky-Witten invariants of log symplectic manifolds [MR 1953353]
- Martin A. Guest – An update on harmonic maps of finite uniton number, via the zero curvature equation [MR 1953354]
- Rei Inoue – The lattice Toda field theory for simple Lie algebras [MR 1953355]
- Hiroshi Konno – On the cohomology ring of the hyperKähler analogue of the polygon spaces [MR 1953356]
- Augustin-Liviu Mare – On the theorem of Kim concerning $QH^*(G/B)$ [MR 1953357]
- Yasuyuki Nagatomo – Geometry of the twistor equation and its applications [MR 1953358]
- Atsushi Nakayashiki – On the cohomology of theta divisors of hyperelliptic Jacobians [MR 1953359]
- Yousuke Ohyama – Isomonodromy deformations and twistor theory [MR 1953360]
- Kaoru Ono – Simple singularities and symplectic fillings [MR 1953361]
- Takashi Otofuji – Quantum cohomology of infinite dimensional flag manifolds [MR 1953362]
- Satoru Saito, Nobuki Suzuki and Hironori Yamaguchi – Discrete conjugate nets of strings [MR 1953363]
- Barbara A. Shipman – Nongeneric flows in the full Kostant-Toda lattice [MR 1953364]
- Ian A. B. Strachan – Frobenius manifolds and bi-Hamiltonian structures on discriminant hypersurfaces [MR 1953365]
- Tetsuya Taniguchi – Periodicity conditions for harmonic maps associated to spectral data [MR 1953366]
- Yuji Terashima – Higher dimensional parallel transports for Deligne cocycles [MR 1953367]
- Hong-Yu Wang – Geometric nonlinear Schrödinger equations [MR 1953368]