Mathematical Sciences: Symplectic and Poisson Geometry

马斯登是世界上最活跃、最富有成效的工人之一。 辛几何和动力系统领域。于合营 与许多合作者合作，他已经开发了非常普遍的 分析哈密顿量的微分几何方法 系统的对称群，并已应用这些一般思想 一系列令人印象深刻的有趣的物理系统。一些 这项工作的突出特点是统一 几何和李理论框架，它提供了详细的 工作的例子，其适用性领域的理论 其中有无限维对称群。 马斯登和他在伯克利和亚利桑那州的合作者将 开展以下主题的研究， 互连：泊松几何和束图; 横截结构、李代数和奇点; 复域微分方程;代数泊松 结构;分叉的几何形状和规范形式 哈密顿系统;哈密顿混沌;相对论性场 理论;调制理论; Kac-Moody李代数和 可积系统

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.