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...

Title: Conditional Positive Definiteness and Complete Monotonicity in Subnormal Operator Theory