Mathematical Sciences: Ergodic Theory and Related Topics

9500803费尔德曼：这个项目涉及到概率论和遍历理论的许多方面的工作。本研究包括以下项目：随机过程过滤的分类；保遍历测度变换下函数均值的零渐近性质共过滤与遍历群作用；欧氏群作用和叶形的再参数化圆上乘法的遍历性质。总的来说，这些项目涵盖了当前遍历理论研究领域的很大一部分。遍历理论一般关注于理解系统的平均长期行为，这些系统过于复杂或混乱，无法实时跟踪。在“动力学”的标题下，可以放置关于变换的重复应用如何影响可测量量的现代理论。这样，变换群和抽象测度论构成了遍历理论的数学基石。这一建议涉及遍历理论数学的前沿。＊＊＊

9500803 Feldman This project involves many facets of work on probability theory and ergodic theory. The research includes work on the following projects: A classification of filtrations of stochastic processes; Zero-one asymptotic properties of averages of functions transformed under ergodic measure preserving transformations; Cofiltrations and ergodic group actions; Reparametrization for Euclidean group actions and for foliations; Ergodic properties of multiplication on the circle. Collectively, these projects cover a broad portion of the current ergodic theory research landscape. Ergodic theory in general concerns understanding the average long-term behavior of systems that are too complicated or chaotic to be followed in real time. Under the heading of "dynamics" can be placed the modern theory of how repeated applications of transformations effect measurable quantities. In this way, groups of transformations and abstract measure theory form the mathematical cornerstones of ergodic theory. This proposal involves the leading edge of the mathematics of ergodic theory. ***