Relations between differential geometry and integrable systems can be traced back more than a century, but it was only recently that methods of integrable system theory have been consistently applied to obtain global geometrical results. These methods include insights gained from soliton theory in the 1970's, ideas obtained from mathematical physics in the 1980's and the sophisticated recent tools from algebraic geometry, representation theory, and the theory of infinite dimensional manifolds.

Some of the major highlights of this area are the remarkable geometry of the KdV equation (and other soliton equations), the analysis of classes of surfaces (such as CMC surfaces and harmonic maps) by means of spectral curves and loop groups, and the theory of discrete integrable systems (aided by state of the art computer visualization and experimentation). Substantial contributions have been and are being made by British mathematicians. The wide spectrum of problems being studied and the pioneering nature of the subject have led to a need for greater cohesion.

Goals

The purpose of this symposium is to bring together leading researchers for a 10 day period of concentration, consolidation and cross-fertilization. This will allow the experience and progress made by each group to support the work of other groups. As the first high profile conference in the UK on this topic, it will greatly strengthen the network of core researchers in the UK. Regional cooperation (identified as a structural issue in the recent International Review of UK Research in Mathematics) will be stimulated as UK researchers in the area of the symposium are spread widely throughout the country.

A further goal is to advance collaboration with Japanese mathematicians, particularly in the areas of constant mean curvature surfaces, soliton equations, and quantum integrable systems, where Japanese expertise and collaborative links with British reseachers already exist.

Organising Committee
Consists of the Programme Committee together with J. Bolton (Durham), R. Miyaoka (Kyushu), Y. Ohnita (Osaka City University), W. Rossman (Kobe).