Mathematical Science: RUI: Actions of Discrete Subgroups of Lie Groups

数学科学：RUI：李群的离散子群的作用

• 批准号: 9214077
• 负责人: Dave Witte
• 金额: $ 9.86万
• 依托单位: Williams College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-11-15 至 1996-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9214077&HistoricalAwards=false
• 关键词: Mathematical; Science; RUI; Actions; Discrete

The classical crystallographic groups of ordinary Euclidean space are basic examples of discrete subgroups of Lie groups. The crystallographic groups arising in the very rigid geometric structures known as locally symmetric spaces of higher rank have been classified by Margulis. Witte will investigate whether these important groups can be realized as symmetries of one-dimensional spaces. Witte will also investigate the crystallographic groups that arise in homogeneous spaces other than the usual symmetric spaces. 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.

普通欧几里得空间的经典晶体学组是谎言组离散亚组的基本示例。 在非常刚性的几何结构中产生的晶体学组被Margulis分类为较高等级的局部对称空间。 维特将研究这些重要群体是否可以实现为一维空间的对称性。 Witte还将研究除通常的对称空间以外的同质空间中出现的晶体学组。 该项目涉及厄贡理论的研究。 一般而言，奇异理论的理解是理解动力学过于复杂或混乱的系统的平均行为，无法在微观细节中遵循。 在标题下“动态可以放置在现代理论上，即抽象转换群如何在平滑空间上作用。以这种方式，厄尔贡理论使与几何形状接触，以寻求对均匀空间进行分类的流量。