Interactions between operator algebras and topological dynamics

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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.