Mathematical Sciences: Dynamics of Unipotent Translations onHomogeneous Spaces

数学科学：齐次空间上的单能平移动力学

• 批准号: 9001737
• 负责人: Marina Ratner
• 金额: $ 9.24万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001737&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; Unipotent; Translations

This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces. Professor Ratner is a world leader in ergodic theory. She will continue her work on the "rigidity" of unipotent subgroups of connected Lie groups. In particular, she will attempt to prove a conjecture of Raghunathan which states that every such subgroup is "algebraic". Such a result would have important implications for the diverse fields of ergodic theory, geometry, and number theory.

这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 动态过于复杂或混乱的系统 在微观细节上进行跟踪。 在“动态”标题下， 现代理论认为， 变换作用于光滑空间。 这样遍历理论 与几何学接触，以寻求对 齐性空间 拉特纳教授是遍历理论的世界领导者。 她 将继续她的工作“刚性”的幂幺子群 连通李群 特别是，她将试图 证明Raghunathan的一个猜想，该猜想指出， 子组是“代数的”。 这样的结果将具有重要意义 对遍历理论、几何学、 和数论