Groups and Operator Algebras Seminar

Speaker: Matthew Kennedy (University of Waterloo)

Title: In this talk, I will introduce noncommutative convexity and present a brief overview of noncommutative Choquet theory, which provides a structural foundation for the study of noncommutative convex sets. Since the category of compact noncommutative convex sets is dual to the category of operator systems, which are unital self-adjoint subspaces of operators, noncommutative Choquet theory can potentially shed new light on problems of an operator-algebraic nature. I will discuss two recent examples of this. The first relates to the notion of self testing in quantum information theory, and the second provides a new characterization of operator systems satisfying an important approximation-theoretic property called hyperrigidity. This talk will feature joint work with Ken Davidson and Eli Shamovich.