Special Colloquium

Paul Skoufranis, Texas A&M University

“Free Probability for Pairs of Faces”

Free probability is a non-commutative probability theory that arises by examining the joint mo- ments of operators acting on the left-hand side of reduced free product spaces. Introduced by Voiculescu in the 1980s, free probability has become an important part of the theory of operator algebras with many applications to random matrix theory.

Last year, Voiculescu introduced the notion of free independence for pairs of faces (also called bi-free independence) in order to simultaneously study the left and right representations of algebras on reduced free product spaces. In this talk, we will survey how the structures of free probability generalize to the bi-free setting and how bi-free probability provides a wealth of new structures to examine.

Refreshments will be served in MC 5158B at 3:30 p.m. Everyone is welcome to attend.