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
wide spectrum of problems
being studied and the
pioneering nature of the subject
have led to a need for greater cohesion.
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.