Mathematical Sciences: Symplectic and Poisson Geometry

这个范围广泛的项目将涉及亚利桑那州和伯克利的研究人员。研究的基本主题是哈密顿系统或泊松结构的概念。将涵盖的主题有可能在数学和物理方面都有重要的应用。这些研究将涵盖以下主题及其相互联系：Poisson几何和丛图；横向结构、李代数和奇点；复域中的微分方程；代数Poisson结构；哈密顿系统的分叉和标准型的几何；哈密顿混沌；调制理论；Kac-Moody李代数和可积系统。

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.