Center for Noncommutative Geometry and Operator Algebras

Functional Analysis/Operator Algebras Seminar, Fall 1999

  • Date: 10/15/99
  • Date: 10/22/99
    • Speaker: Alexis Alevras, UCSB
    • Title: On the classification of continuous semigroups of endomorphisms of B(H)
    • Abstract:
      Given a symmetric operator on a Hilbert space, the question of existence
      of selfadjoint extensions is answered by a classical index theorem of
      von Neumann. This question is quite important e.g. when one needs to
      know whether a Hamiltonian can be extended to a self adjoint operator,
      thereby defining the dynamics of a quantum mechanical system.
      In the modern formulation of quantum mechanics the Hamiltonian
      is replaced by a derivation on the algebra of observables and the
      problem is whether such a derivation defines the time evolution of the system.
      In the talk I will give an overview of an index theory for one
      parameter semigroups of endomorphisms of B(H) relating
      to this question, which can be viewed appropriately as a quantized
      analogue of the Fredholm index of maximal symmetric operators.
  • Date: 10/29/99
    • Speaker: Perturbation Theory of Banach Space Complexes
    • Title: Jim Gleason, UCSB
    • Abstract:
      The theory of Fredholm operators has been well studied with
      many important results. One of these results is the stability of
      Fredholmness and the index under certain types of perturbations. We will
      discuss the extension of this theory to the context of Banach space
      complexes.
  • Date: 11/5/99
    • Speaker: Alexis Alevras, UCSB
    • Title: Topological entropy (after Voiculescu and Brown), Part I
  • Date: 11/11/99, Mathematics Colloquium!
    • Speaker: Marc Rosso, Universite Louis Pasteur (Strasboug) and MSRI
    • Title: Quantum groups and quantum shuffles
    • Abstract:
      We will describe an elementary construction of quantum groups in terms of a
      deformation of the shuffle algebra on a finite dimensional vector space.
      This allows for a construction of representations in terms of iterated
      integral and for a construction of Poincare-Birkhoff-Witt type bases via
      the combinatorics of Lyndon words.
  • Date: 11/12/99, Engineering Department, Seminar talk, 3 pm
    • Speaker: Ciprian Foias, Indiana University
    • Title: Using Camassa-Holm equations to predict turbulent flows in channels and pipes
    • Abstract:
      Survey of the approach developed by S. Chen, C. Foias, D.D. Holm, E. Olson,
      E.S. Titi and S. Wynne in the study of turbulent flows in channels and
      pipes based on the viscous Camassa-Holm equations. This approach seems to
      yield accurate predictions for the mean velocity profiles of turbulent
      flows in pipes for very large Reynolds numbers. (See Physica D, 133(1999),
      49-65.)
  • Date: 11/12/99
    • Speaker: Alexis Alevras, UCSB
    • Title: Topological entropy (after Voiculescu and Brown), Part II
  • Date: 11/19/99
    • Speaker: Mihai Putinar, UCSB
    • Title: Pade approximation via operator theory
    • Abstract:
      A new proof of Markov convergence theorem will be given as a consequence
      of von Neumann’s theory of spectral sets. Other rational convergence
      results will be derived from the classical spectral theory of compact
      operators.
  • Date: 11/26/99
    • no meeting (Thanksgiving Holiday)
  • Date: 12/3/99
    • Speaker: Anne Louise Svendsen, UCSB
    • Title: Principal graphs of subfactors with small Jones index (after Haagerup)
    • Abstract:
      The principal graph of a subfactor encodes the principal part of the
      fusion algebra of bimodules associated to a subfactor. These graphs
      are weighted, bipartite, possibly infinite graphs with a distinguished
      vertex and they reflect a part of the algebraic information contained
      in the standard invariant of a subfactor. Haagerup has produced a complete
      list of possible principal graphs of irreducible subfactors with Jones index
      between 4 and 3 + \sqrt{3} and we will discuss in this talk
      Haagerup’s results and the combinatorial/computational methods used
      to obtain them.
  • Date: 12/10/99
    • Speaker: Dietmar Bisch, UCSB
    • Title: Obstructions for principal graphs via planar algebra techniques (after Jones)
    • Abstract:
      The higher relative commutants of a subfactor are modules for
      the affine Temperley-Lieb-Jones algebras. This fact gives strong
      constraints on the possible structure of the standard invariant of
      a subfactor and we will explain in this talk how this point of view can
      be used to obtain the well-known obstructions for subfactors with small
      Jones index.

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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