Operator algebra seminar

Speaker: Raphaël Clouâtre (University of Manitoba)

Title: Choquet theory on state spaces of C*-algebras and the hyperrigidity conjecture

Abstract: Fifty years ago, Arveson initiated an ambitious program to analyze non self-adjoint operator algebras through the lens of C*-algebras. The so-called C*-envelope was the centrepiece of Arveson's vision, and it has since become a ubiquitous tool in modern operator algebras. At the heart of its construction is a fruitful analogy with the classical Choquet boundary of a function algebra.

In 2011 a tantalizing question was raised, asking whether this non-commutative Choquet boundary could detect a striking rigidity property of the C*-envelope. The difficulty in settling this open problem lies partly in the fact that the ``non-commutative boundary points" are *-representations, and are thus poorly adapted to the standard tools of Choquet theory. In this talk, I will consider a linearization of Arveson's analogy, wherein *-representations are replaced with states. I will illustrate how this new perspective can be used to gain insight into what is now known as Arveson's hyperrigidity conjecture.