Colloquium Announcement: A Brief Overview of Bi-Free Probability (Dr. Paul Skoufranis)
A Brief Overview of Bi-Free Probability
Department of Mathematics and Statistics Colloquium Announcement
Date: Friday December 2nd 2016
Place: ARTS Building Room 101
Time: 3:30 PM
Title: A Brief Overview of Bi-Free Probability
Guest Speaker: Dr. Paul Skoufranis, York University
Abstract: Free probability is a non-commutative probability theory that studies the joint moments of operators acting on reduced free products of vector spaces. Since its inception by Voiculescu in the 1980s as an attempt to solve the isomorphic free group factor problem, free probability has become an important part of the theory of operator algebras with several applications to random matrix theory.
In this talk, after a general introduction to the ideas and concepts of free probability, we will provide a brief overview of the recent extension of free probability known as bi-free probability. Bi-free independence extends the notion of free independence in order to simultaneously study the left and right regular representations on free products of vector spaces. Our overview will look at topics such as basic de nitions, bi-free cumulants, bi-free in nitely divisible distributions, operator-valued bi-free independence, bi-free matrix models, and bi-free partial transformations.