Groups and Operator Algebras Seminar

Speaker: Arnaud Brothier (University of Trieste)

Title: Moduli spaces of representations of the Cuntz algebra

Abstract: In his quest in constructing conformal field theories from subfactors Vaughan Jones found an unexpected connection with Richard Thompson's group T. This led to Jones' technology: a powerful method for constructing actions of certain groups. I will introduce the great lines of this fascinating connection. I will then explain how this approach permits to promote representations of certain basic algebras to more complicated ones like the Cuntz algebra. Thanks to some rigidity phenomena this will provide moduli spaces of irreducible classes of representations of the Cuntz algebra. These are joint works with Vaughan Jones and with Dilshan Wijesena.