Mathematical Sciences: Topological Invariants Associated to C*-Dynamical Systems

威廉姆斯将继续他的调查理想结构的交叉产品C*-代数。 主要的重点将是拓扑不变量之间的相互作用与动力系统和结构所产生的交叉产品。 该项目涉及遍历理论的研究。 遍历理论一般涉及理解系统的平均行为，其动力学过于复杂或混乱，以至于无法在微观细节中遵循。 在“动力学”的标题下，可以放置抽象变换群如何作用于光滑空间的现代理论。 通过这种方式，遍历理论在对齐次空间上的流进行分类的探索中与几何学发生了联系。

Williams will continue his investigation of the ideal structure of crossed product C*-algebras. The primary focus will be on the interplay between topological invariants associated to a dynamical system and the structure of the resulting crossed product. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way, ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.