Mathematical Sciences: Symplectic and Poisson Geometry

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Marsden is one of the most active and productive workers in the field of symplectic geometry and dynamical systems. In joint work with many collaborators, he has developed very general differential geometric procedures for analyzing Hamiltonian systems with symmetry groups, and has applied these general ideas to an impressive range of physically interesting systems. Some outstanding characteristics of this work are the unified geometric and Lie theoretic framework it provides, the detailed working out of examples, and its applicability to field theories where one has infinite dimensional symmetry groups. Marsden and his collaborators at Berkeley and Arizona will carry out research into 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; relativistic field theories; modulation theory; Kac-Moody Lie algebras and integrable systems.