Ontario operator algebras online seminar - past seminars
Monday Sep. 21, 3-4pm (EDT).
David Kerr (TAMU) - Entropy, orbit equivalence, and sparse connectivity
Abstract. It was shown by Tim Austin that if an orbit equivalence between probability-measure-preserving actions of finitely generated amenable groups is integrable then it preserves entropy. I will discuss some joint work with Hanfeng Li in which we show that the same conclusion holds for the maximal sofic entropy when the acting groups are countable and sofic and contain an amenable w-normal subgroup which is not locally virtually cyclic, and that it is moreover enough to assume that the Shannon entropy of the cocycle partitions is finite (what we call Shannon orbit equivalence). It follows that two Bernoulli actions of a group in the above class are Shannon orbit equivalent if and only if they are conjugate. We also establish a topological version of our measure entropy invariance result, and I will present an application of this to the construction of C*-simple groups whose group von Neumann algebras has property Gamma, which is part of a joint project with Robin Tucker-Drob.
Nov. 3, 1:30-2:30 (EST).
Alcides Buss (UFSC) - Amenable actions of locally compact groups on C*-algebras
Abstract. I will talk about joint work with Siegfried Echterhoff and Rufus Willett in which we introduce and study amenable actions of locally compact groups on C*-algebras, building on previous similar notions by Anantharaman-Delaroche for actions of discrete groups. Among the new results we prove an extension of Matsumura’s theorem giving a characterization of the weak containment property (coincidence of full and reduced crossed products) for actions on commutative C*-algebras and give examples showing that this result does not extend to general noncommutative C*-algebras.
Dec. 1, 1:30-2:30 (EST).
Gilles Pisier (TAMU) - Lifting: from local to global?
Abstract. The talk will discuss several instances of the problem whether a local lifting property implies a global one for C*-algebras.
In the first part we describe the class of von Neumann algebras that are seemingly injective in the following sense: there is a factorization of the identity of M through some B(H) via unital positive contractive maps. If M has a separable predual and is not nuclear, M is isomorphic (as a Banach space) to B(H) (with H separable). For instance this applies (rather surprisingly) to the von Neumann algebra of any free group. The proof uses positive local liftings. In the (probably shorter) second part we discuss the global lifting property for C*-algebras.