Interactions between operator algebras and topological dynamics

这个项目的目标是发展一个更好的理解的概念，连续轨道等价的拓扑动力系统。这个新概念以前没有被详细研究过，有许多有趣而重要的问题还没有很好地理解，例如刚性现象。除了从动力学的角度来看，连续轨道等价本身是有趣的，它还与几何群论中的拟等距和C*-代数中的嘉当子代数的概念密切相关。因此，我们预计，在这个项目的背景下取得的进展将产生重要影响，建立一个富有成效的相互作用之间的运营商代数，拓扑动力学和几何的群体。

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.