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

DMS-9424613 PI：Margulis 马古利斯将调查的动态分组行动均匀空间与应用数论，适当的不连续群体作用于均匀空间，刚性问题和相关问题的几何和遍历理论，几何方面的减少理论。 李群理论是以挪威数学家Sophus Lie的荣誉命名的，是世纪数学的重要课题之一。 李群表示论作为利用系统中固有对称性的数学工具，对数学本身，特别是分析和数论，以及理论物理学，特别是量子力学和基本粒子物理学产生了深远的影响。

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.