Title: Von Neumann equivalence and group approximation properties

Abstract: One of the themes in measured group theory is studying the stability of group approximations properties such as amenability, Haagerup property, property (T) etc. under measure equivalence which is an equivalence relation on the the class of groups. Not a long time ago the notion of von Neumann equivalence, which generalizes measure equivalence, was introduced by Jesse Peterson, Lauren Ruth, and myself. In this talk I will discuss the stability of some group approximation properties under von Neumann equivalence.