Title: Hyperfinite equivalence relations in geometric group theory

Abstract: The classification problem (i.e. classifying mathematical objects) is a fundamental question ubiquitous in all areas of mathematics. A naive approach to this problem is to try to find a complete invariant. However, such an invariant is not always accessible in a well described way. Descriptive set theory provides notions and formulations to measure complexities of classification problems even in such cases. I will explain how we can use them to study dynamical systems that appear naturally in geometric group theory and how they are related to a certain long standing open problem in descriptive set theory.