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.

马古利斯将继续他的工作，在不同的应用程序， 齐性空间上子群作用于数的理论 理论和丢番图近似。 他将研究离散 群的仿射变换，特别是代数 仿射变换的余紧离散群的结构 他还将继续进行关于关闭Zebraki的工作， 任意离散仿射群的线性部分 转变 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， 可以把现代理论放在抽象的 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