Paul Skoufranis

About

After completing my B. Math (Honours and Co-operative programs, minoring in Physics) at the University of Waterloo in Ontario, Canada in Spring 2009, I moved to UCLA to pursue my doctoral degree.  Working under the advisement of Dimitri Shlyakhtenko, I was awarded a Ph.D. (Mathematics) in June 2014.  Subsequently I spent two years as Visiting Assistant Professor in the Mathematics Department at Texas A&M University under the supervision of Ken Dykema.  Since July 2016, I have been a professor at York University first at the Assistant Professor level until July 2020 where I was promoted to an Associate Professor with tenure.

My research interests lie in the branch of functional analysis known as operator algebras.  Specifically, my research projects thus far have been focused in two areas, namely free probability and operator theory.  I endeavour to continue to work in both areas and have desires to broaden my research interests to other parts of functional analysis.

My most recent projects in free probability have come from studying a recent extension of free probability known as bi-free probability.  The goal of said work is to understand, extend, and examine the differences between freeness and bi-freeness, where things become severely more complicated in the latter.

My projects in operator theory have come from studying matricial problems in a wide range of infinite dimensional settings.  My most recent work stems from studying a notion of majorization for self-adjoint operators and understanding the role it plays with regards to convex hulls of unitary orbits and Schur-Horn theorems in various C*-algebras.

Education

1. UCLA, Los Angeles, California, September 2009 – June 2014
   • Ph.D. (Mathematics)
   • Thesis Advisor: Dimitri Shlyakhtenko
2. University of Waterloo, Waterloo, Ontario, September 2004 – April 2009
   • Bachelor of Mathematics, Honours Pure Mathematics-Physics Minor,
   • Co-operative Program, (with Distinction – Dean’s Honour List)

Sub-Discipline

Operator Theory, Free Probability, Operator Algebras, C*-Algebras, Functional Analysis

Research Areas