Groups and Operator Algebras Seminar

Speaker: Ian Thompson

Title: Rigidity of Operator Systems

Abstract: We explore various ways an operator system determines (or, is rigid in) its generating C*-algebra. Central to this mission is a conjecture of Arveson, who asserted that the strongest notion of rigidity is equivalent to an (a priori) much weaker condition. Arveson’s conjecture has been reformulated in many ways, seen connections to other conjectures in operator theory, and verified for large classes of examples that offer varied behaviour. Yet, despite this positive progress, Arveson’s conjecture has just recently been disproven by Bilich and Dor-On. Moreover, the counterexample that was found is not overly pathological or exotic, suggesting that there may be something intrinsically missing in Arveson’s original formulation of the conjecture. Here, we will present an amended version of Arveson’s conjecture; thereby allowing for principles of classical approximation theory to be extended to non-commuting variables. This is based on joint work with Raphaël Clouâtre.