Operator Algebras and Dynamics Seminar
Fall 2018
All talks are from 3:454:45 p.m. in the Seminar room, unless otherwise specified.

Nov05

Tanner CrowderNRLTime: 03:45 PM

Oct01

Faithfulness vs. Uniqueness, for PseudoExpectationsVrej ZarikianUSNATime: 03:45 PM

Sep24

Faithfulness vs. Uniqueness, for PseudoExpectationsVrej ZarikianUSNATime: 03:45 PM

Sep17

Approximate Transitivity of the Natural Action of Finite Permutations of N on {0,1}^NMitch BakerUSNATime: 03:45 PM
View Abstract
In 1980, Connes and Woods introduced the notion of approximate transitivity (AT) for dynamical systems arising in the context of von Neumann algebras (i.e. Connes’ flow of weights) – for the purpose of characterizing which approximately finite dimensional factors could be written as an infinite tensor product of type I factors (ITPFI). The latter had played a major role in the development of the theory of von Neumann algebras, but their connection to general factors had long remained mysterious. Later on, straightaway dynamical systems researchers investigated how this property related to properties studied in the context of standard dynamical systems (e.g. entropy, rank one, etc.), obtaining some interesting results  but so far proving approximate transitivity has been quite difficult, and relatively few classes are known even now. We present a new infinite class of natural dynamical systems arising from product spaces and the classical action of permutations of finite length on them (originally motivated by our study of groupinvariant type III factors and their flow of weights), and show that they are approximately transitive.

Sep10

Approximate Transitivity of the Natural Action of Finite Permutations of N on {0,1}^NMitch BakerUSNATime: 03:45 PM
View Abstract
In 1980, Connes and Woods introduced the notion of approximate transitivity (AT) for dynamical systems arising in the context of von Neumann algebras (i.e. Connes’ flow of weights) – for the purpose of characterizing which approximately finite dimensional factors could be written as an infinite tensor product of type I factors (ITPFI). The latter had played a major role in the development of the theory of von Neumann algebras, but their connection to general factors had long remained mysterious. Later on, straightaway dynamical systems researchers investigated how this property related to properties studied in the context of standard dynamical systems (e.g. entropy, rank one, etc.), obtaining some interesting results  but so far proving approximate transitivity has been quite difficult, and relatively few classes are known even now. We present a new infinite class of natural dynamical systems arising from product spaces and the classical action of permutations of finite length on them (originally motivated by our study of groupinvariant type III factors and their flow of weights), and show that they are approximately transitive.