Orateur
Description
Stability asks whether approximate solutions of algebraic relations can be perturbed to exact solutions. In C-algebra theory, stability questions have a long history, motivated in part by classical problems in operator theory, and have become useful tools for studying the structure of C-algebras.
For groups, stability asks whether approximate representations are close to genuine representations. Different notions arise depending on the target groups and the chosen metrics, such as the Hilbert–Schmidt or operator norm metrics on unitary groups and the Hamming metric on symmetric groups. In recent years, interest in group stability has grown considerably, partly because of its connections with approximation problems for groups.
This minicourse will introduce stability in C*-algebras and groups and explore the connections between these settings, with particular emphasis on the role of operator algebraic methods in the study of group stability.