Interactions between operator algebras and topological dynamics

本课题的目的是为了更好地理解拓扑动力系统的连续轨道等价的概念。这个新概念以前没有被详细研究过，并且有许多有趣和重要的问题没有被很好地理解，例如刚性现象。除了从动力学的角度来看，连续轨道等价本身就很有趣外，它还与几何群论中的拟等距概念和C*-代数中的Cartan子代数密切相关。因此，我们期望在本项目背景下取得的进展将对建立算子代数，拓扑动力学和群几何之间富有成效的相互作用产生重要影响。

The goal of this project is to develop a better understanding of the concept of continuous orbit equivalence for topological dynamical systems. This new notion has not been studied in detail before, and there are many interesting and important questions which are not well-understood, for instance rigidity phenomena. Apart from being interesting on its own right from the point of view of dynamics, continuous orbit equivalence is also closely related to the concepts of quasi-isometry in geometric group theory and Cartan subalgebras in C*-algebras. Hence we expect that progress made in the context of this project will have an important impact on establishing a fruitful interplay between operator algebras, topological dynamics and the geometry of groups.