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Report Chung 2015

"It is a great opportunity for me to receive a travel grant from International Mathematical Union-Simons Foundation to visit Professor Wilhelm Winter at University of Muenster, Germany from May 16, 2015 to July 16, 2015. The main purpose of my visit is to study connections between dynamical systems and the classification program of C*-algebras via the Focus Programme on C*-algebras at University of Muenster.

I participated in the weekly seminar organized by the group of Professor Wilhelm Winter.
During this visit at Muenster, I presented two talks: the first one is on June 23, 2015 at Oberseminar C*-algebras with the title “Rigidity of algebraic actions”; and the second one is “Dynamical properties and algebraic properties of algebraic actions” at the workshop on “C*- algebras, Geometry and actions”, July 13-17, 2015. In addition to discussions with Professor Wilhelm Winter, I have had many useful discussions about dynamical systems and C*-algebras with Ph.D student Gábor Szabó, post-doctoral fellows Huichi Huang, Nicolai Stammeier, Jianchao Wu, visiting scholars David Kerr, Xin Li, Norio Nawata, Christopher Phillips and Yuhei Suzuki.

Although my original research plan for this visit about mean dimension and crossed product C*-algebras does not proceed well as I expected, we get some progress on two other projects related with rigidity of dynamical systems after this fruitful visit. We obtain some preliminary results for topological rigidity of certain algebraic actions and rigidity of continuous cocycles of Bernoulli shifts for certain groups. We will investigate further rigidity of algebraic actions in measurable setting and for the project about continuous orbit equivalence, cocycles and rigidity, we will explore other systems such as profinite actions, shifts of finite type, and their applications in C*-algebras.

I would like to thank IMU-Simons foundation for the travel support and Professor Wilhelm Winter for a warm hospitality during my visit at Mathematical Institute, University of Muenster."

- Nhan-Phu Chung