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: 9424613
• 负责人: Gregory Margulis
• 金额: $ 25.52万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424613&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Geometric; Ergodic

DMS-9424613 PI: Margulis Margulis will investigate the dynamics of subgroup actions on homogeneous spaces with applications to number theory, properly discontinuous groups acting on homogeneous spaces, rigidity questions and related problems in geometry and ergodic theory, and geometric aspects of reduction theory. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.

DMS-9424613 PI：Margulis Margulis将调查针对数字理论应用的同质空间的亚组动作的动力学，适当的不连续的群体，作用于同质空间，刚性问题，几何学和相关问题的几何学和赤道理论的相关问题，以及还原理论的几何方面。 以纪念挪威数学家索菲斯谎言而命名的谎言理论一直是20世纪数学的主要主题之一。 作为利用系统固有的对称性的数学工具，谎言组的表示理论对数学本身，尤其是分析和数理论以及理论物理学，尤其是量子力学和基本粒子物理学产生了深远的影响。