Linear Analysis Seminar
Date: March 1, 2019
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Roy Araiza, Purdue University
Title: On operator systems and matrix convexity
Abstract: Operator systems (self-adjoint unital subspaces of C*-algebras) had been looked as early as the 1970's. As early as the 1980's, operator algebraists realized that there was a rich theory in noncommutative convexity (matrix convexity). Though it was not until 1999 that it was noticed by Webster and Winkler that operator systems and compact matrix convex sets were intimately connected. Using Webster-Winkler duality and noncommutative Choquet theory, we have been able to present a new way in looking at Choquet points of finite-dimensional compact matrix convex sets. We will begin by reviewing noncommutative convex theory and Webster-Winkler duality. Operator system tensor products will be reviewed (if needed). As time permits we will then discuss Choquet points of finite-dimensional compact matrix convex sets. This is joint work with Adam Dor-On and Thomas Sinclair.