Functional Analysis/Operator Algebras Seminar, Fall 1999

• Date: 10/15/99
  • West Coast Operator Algebra Symposium, University of Victoria, Canada (Oct. 16, 17, 1999)

• 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.