On the structure of group C*-algebras

Group C*-algebras are important examples in the theory of operator algebras and at the same time an indispensable tool in unitary representation theory. In recent years, significant progress in understanding their structure has been made. In this talk, I will focus on results and open problems about group C*-algebras with stable rank one. After a gentle introduction to group C*-algebras and the notation of stable rank, I will present the state-of-the-art, open problems and common methods, which are related to geometric group theory and harmonic analysis.