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

9424613 PI：Marguis Marguis将通过应用数论研究齐次空间上的子群作用的动力学，齐次空间上作用的适当不连续群，几何和遍历理论中的刚性问题和相关问题，以及约化理论的几何方面。李群理论是以挪威数学家索菲斯·李的名字命名的，一直是20世纪数学的主要主题之一。作为利用系统固有对称性的数学工具，李群的表示理论对数学本身，特别是在分析和数论方面，以及对理论物理，特别是量子力学和基本粒子物理，都产生了深远的影响。

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.