Mathematical Sciences: Symplectic and Poisson Geometry

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This wide-ranging project will involve researchers at both Arizona and Berkeley. The underlying theme of the research is the concept of Hamiltonian system or Poisson structure. The topics to be covered have the potential for significant applications to both mathematics and physics. The investigations will cover the following topics and their interconnections: Poisson geometry and the bundle picture; transverse structures, Lie algebras, and singularities; differential equations in the complex domain; algebraic Poisson structures; geometry of bifurcations and normal forms of Hamiltonian systems; Hamiltonian chaos; modulation theory; Kac- Moody Lie algebras and integrable systems.