Vorträge in der Woche 04.12.2006 bis 10.12.2006

Montag, 04.12.2006: Integrable Systeme in der Geometrie

Dr. Josef Dorfmeister

Many geometric objects are defined by highly non-linear partial differential equations, like surfaces of constant mean curvature, Willmore surfaces, isometric immersions of space forms, holomorphic curves in the 6-sphere, and Hamiltonian stationary Lagrangian surfaces. These quite different geometric objects have the common feature that they are contained in a loop of objects of the same type. Some Birkhoff splitting relative to the loop parameter leads to a potential, which satisfies an integrability condition (usually the one of a curved flat), which is much simpler than the integrability condition of the original geometric object. In some cases the integrability condition for the potential is actually trivial, while the integrability condition for the original geometric object is highly non-trivial. The special feature of this approach is that in all the cases mentioned above it is possible to reconstruct the original geometric object from its potential.