Title: Group stability
Abstract: In 1940, Ulam asked the following general question, usually referred to as "Ulam’s stability problem": given two algebraic structures Γ and G and an approximate homomorphism f : Γ → G, is f close to a homomorphism? The answer depends on Γ and G as well as the chosen notions of an approximate homomorphism and proximity between functions.
This talk consists of two parts:
First, we survey some new and classical results in stability theory and tie them to approximation problems of algebraic structures, specifically soficity and Connes' embedding problem.
Then, we discuss the stability of actions on finite sets. This part is based on a joint work with Oren Becker.