Mathematical Sciences: Arithmetic, Geometric, and Ergodic Aspects of the Theory of Lie Groups and Their Discrete Subgroups

数学科学：李群及其离散子群理论的算术、几何和遍历方面

• 批准号: 9204270
• 负责人: Gregory Margulis
• 金额: $ 21.83万
• 依托单位: Yale University
• 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: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204270&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Geometric; Ergodic

Margulis will continue his work on different application of the theory of subgroup actions on homogeneous spaces to number theory and Diophantine approximations. He will study discrete groups of affine transformations, and in particular the algebraic structure of cocompact discrete groups of affine transformations. He will also continue his work on the Zariski closure of the linear part of an arbitrary discrete group of affine transformations. 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.

Margulis将继续他在数字理论和二磷酸近似值的均相空间中的亚组作用理论的不同应用方面的工作。 他将研究仿生转化的离散组，尤其是仿射转化组的离散组的代数结构。 他还将继续在任意离散的仿射转换组的线性部分的Zariski关闭方面的工作。 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。