A metric characterization of freeness

Explanation

A series of research talks in April 2024 at the SNU Operator Seminar

Title

A metric characterization of freeness

Abstract

The Free Probability theory is a branch of operator algebra theory studying a non-commutative analogy of independence in classical probability theory. Although it mainly deals with analytical objects, its definition and properties are usually algebraic and combinatorial. However, in 2021, L. Cadilhac and B. Collins discovered an analytical necessary and sufficient condition of freeness for Haar unitary elements in a finite von-Neumann algebra. The purpose of these talks is to give details of this characterization.