Title: Stability and lifting properties for groups and their C*-algebras

Abstract: We will discuss the notion of Hilbert-Schmidt stability for groups, including the definition, motivation, examples and some basic properties. We will then establish a cohomological obstruction to Hilbert-Schmidt stability for certain property (T) groups. Finally, we will relate this to some other stability and lifting properties, like the (local) lifting property of the group C*-algebra. This is partially based on joint work with Adrian Ioana and Matthew Wiersma.