Mathematical Sciences: Ergodic Theory, Groups, and Geometry

数学科学：遍历理论、群和几何

• 批准号: 9107285
• 负责人: Robert Zimmer
• 金额: $ 27万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107285&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Ergodic; Theory; Groups

Professor Zimmer will study a variety of questions within the general program of understanding the actions of semisimple Lie groups and their discrete subgroups on manifolds. This includes an investigation of the topological, geometric, and analytic properties of manifolds admitting such an action, and the measure theoretic, topological, and geometric structure of the actions themselves. The techniques of ergodic theory and algebraic groups, combined with the geometric structure inherent in the situation, will be essential throughout the work. This award will also support three junior investigators who will conduct research in the same general area. Groups usually arise as transformations which preserve the symmetry of some system much as the group of rotations preserves the symmetry of a sphere. Given an abstract group there are often many ways it can be realized or represented as a group of transformations. There has been much research done on the representation of groups as linear transformations on a vector space. It is in the still unchartered realm of nonlinear actions of groups on curved surfaces or manifolds where Professor Zimmer's research will take place.

齐默教授将研究各种问题， 理解半单李作用的一般程序 群及其在流形上的离散子群。 这包括 拓扑学、几何学和分析学的研究 流形的性质承认这样的行动，和措施， 动作的理论、拓扑和几何结构 自己 遍历理论和代数群的技巧， 结合该情况固有的几何结构， 在整个工作中都是必不可少的。 该奖项还将 支持三名初级调查员，他们将在 相同的区域。 群通常是作为保持 某些系统的对称性与旋转群的对称性一样 球体的对称性 给定一个抽象的组， 它可以以多种方式实现或表示为一组 转变 有很多研究都是关于 向量上线性变换的群表示 空间 这是在非线性行为的领域仍然是未知的 在曲面或流形上的群， 将进行研究。