Group Stability and Quantum Information Theory

The main focus of the project will be on stability properties for groups and their connections with quantum information theory. Intuitively, the term stability refers to the phenomenon of when approximate properties are ""close"" to actual properties. Concretely, the project will introduce for the first time stability with respect to quantum groups, and provide a systematic approach towards different important notions of stability for various classes of groups, notably ""graph product-like"" groups and amenable groups. For the latter, stability is also connected to character theory and dynamical systems, which will allow for different techniques from these areas to be applied towards our results.""