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Mathematics Department

Operator Algebras and Dynamics Seminar

Fall 2018

All talks are from 3:45-4:45 p.m. in the Seminar room, unless otherwise specified.

  • Nov
    05
  • Tanner Crowder
    NRL
    Time: 03:45 PM
  • Oct
    01
  • Faithfulness vs. Uniqueness, for Pseudo-Expectations
    Vrej Zarikian
    USNA
    Time: 03:45 PM
  • Sep
    24
  • Faithfulness vs. Uniqueness, for Pseudo-Expectations
    Vrej Zarikian
    USNA
    Time: 03:45 PM
  • Sep
    17
  • Approximate Transitivity of the Natural Action of Finite Permutations of N on {0,1}^N
    Mitch Baker
    USNA
    Time: 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, straight-away 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 group-invariant type III factors and their flow of weights), and show that they are approximately transitive.
  • Sep
    10
  • Approximate Transitivity of the Natural Action of Finite Permutations of N on {0,1}^N
    Mitch Baker
    USNA
    Time: 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, straight-away 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 group-invariant type III factors and their flow of weights), and show that they are approximately transitive.
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