Ergodic Theory, Groups, and Geometry

摘要9705712 Robert J. Zimmer 本项目的目标是在研究半单李群及其离散子群在流形上的作用的一般程序中研究各种mf问题。 这包括调查的拓扑，几何和分析功能的空间上，这些团体的行为，以及相应的功能的行动本身。 这些问题的应用遍历理论和微分几何也将研究。 代数遍历理论的技术，即，遍历理论与代数群的相互作用，结合微分几何，将 在整个项目中使用。 对称性的研究在数学及其应用中起着基础性的作用。 在数学中，它已被理解为大多数学科的中心主题之一，它的应用范围广泛，如粒子物理学，高效网络设计，编码和雷达。 该项目旨在通过研究存在大对称群的情况来促进这一总体发展，在许多情况下，这正是应用最多的情况。

Abstract 9705712 Robert J. Zimmer The goal of this project is to study a variety mf questions within the general program of investigating actions of semisimple Lie groups and their discrete subgroups on manifolds. This includes an investigation of the topological, geometric, and analytic features of the spaces on which these groups act, and the corresponding features of the actions themselves. Applications of these questions to ergodic theory and differential geometry will be studied as well. The techniques of algebraic ergodic theory, i.e., the interaction of the ergodic theory with algebraic groups, in conjunction with differential geometry, will be used throughout the project. The study of symmetry has played a fundamental role in mathematics and its applications. Within mathematics it has become understood as one of the central themes of most disciplines, and it has had applications as diverse as particle physics, design of efficient networks, coding, and radar. This project aims to contribute to this general development by the study of situations in which there is a large symmetry group, in many cases exactly the situation in which applications are most present.