Stability for C*-algebras and groups

This project focuses on stability problems arising in the areas of Operator Algebras, Group Theory, and Quantum InformationTheory.In the area of Operator Algebras stability techniques provide powerful tools in investigating structure propertiesof operator algebras and are used in the classification program for C*-algebras.

Group-theoretical stability appeared long ago in the study of geometrical structures.

However it became a subjectof particular interest in the very last years because it was found out to have connections with important conjectureson sofific and hyperlinear approximations of groups.The proposed research is aimed to study stability of groups by operator algebraic means.

The focus will be givento developing invariants and criteria for stability of important classes of discrete and locally compact groups andto connections with approximation problems for groups.

Furthermore, on the Operator Algebras side, we plan asystematic study of permanence properties of the class of stable C*-algebras and we plan to explore stability of concrete classes of operator algebras and apply our results to problems from Noncommutative Topology.A part of the project will be devoted to applications of operator-algebraic stability to Quantum Information Theory, namely to the study of overlapping cubits and the superactivation effect for zero-error capacities.