Geometric Aspects of the Einstein Equations and Integrable Systems

Exact solutions in gauge theory, general relativity, and their supersymmetric extensions.- Symmetries and solutions of the einstein equations.- Superposition of solutions in general relativity.- Gauge fields, gravitation and Kaluza-Klein theory.- Gravitational shock waves.- Soliton surfaces and their applications (soliton geometry from spectral problems).- Completely integrable systems of evolution equations on KAC moody lie algebras.- Integrable lattice systems in two and three dimensions.- Isovectors and prolongation structures by Vessiot's vector field formulation of partial differential equations.- Hamiltonian flow on an energy 240 years after the euler-maupertuis principle.