Center for Noncommutative Geometry and Operator Algebras

Operator Algebras Seminar, Winter 1997

  • Date: 1/16/97 (Mathematics Colloquium)
    • Speaker: Sorin Popa, UCLA
    • Title: Amenability in the theory of subfactors
    • Abstract:
      Vaughan Jones proposed in the early 80’s the study of inclusions of
      certain algebras of operators (or subfactors), which arise naturally
      as algebras of symmetries in quantum physics, and proved some
      suprising rigidity results. A rich theory has developed since then
      with many interesting and fruitful connections to other areas of
      mathematics (e.g. knot theory) and theoretical physics (e.g. conformal
      field theory).

      A subfactor can be viewed as a group like object and a variety of
      techniques and concepts extensively used in group theory have
      counterparts in the theory of subfactors and play a crucial role
      there. We will explain in this talk the concept of amenability in
      the theory of subfactors and we will show how it leads to profound
      theorems about the structure of subfactors. We will start with a
      discussion of the different descriptions of amenability for groups,
      such as Kesten’s theorem, and show how it can be extended to operator
      algebras in a natural way.

  • Date: 1/17/97
    • Speaker: Darren Long, UCSB
    • Title: The beginner’s guide to the nonfaithfulness of the Burau representation
  • Date: 1/24/97
    • no meeting this week (because of the MSRI workshop on Vassiliev invariants)
  • Date: 1/31/97
    • Speaker: Raymond Lickorish, Cambridge University (visiting UCSB)
    • Title: Skein theory – How algebras occur in knot theory
  • Date: 2/7/97
    • no meeting
  • Date: 2/14/97
    • no meeting
  • Date: 2/21/97
    • Speaker: Corran Webster, UCLA
    • Title: The Krein-Milman Theorem in Operator Convexity
    • Abstract: We generalize the Krein-Milman theorem to the setting of
      matrix convex sets of Effros-Winkler, extending the work of Farenick-Morenz
      on compact C*-convex sets of matrices and matrix state spaces of C*-algebras.
      (Joint work with Soren Winkler).
  • Date: 2/28/97
    • Speaker: Teodor Banica, Universite de la Mediterranee, CNRS
    • Title: Some examples of compact quantum groups
  • Date: 3/7/97
    • Speaker: Feng Xu, UCLA
    • Title: “Exceptional” subfactors and integrable models
    • Abstract: In this talk I will describe how various puzzles about
      exceptional subfactors and integrable lattice models can be resolved in the
      framework of constructive quantum field theory in two dimensions.
      The relation of such a theory to low-dimensional toplogy and quantum
      groups will also be briefly mentioned.

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Contact

Noncommutative Geometry and Operator Algebras
Department of Mathematics
Vanderbilt University
Stevenson Center 1326
Nashville, TN 37240
U.S.A. Phone: (615) 322-6672
Fax: (615) 343-0215
E-mail: ncgoa[at]vanderbilt[dot]edu