Organizer: Dietmar Bisch

• Date: 4/5/01 (Thursday)
  • Speaker: Alexis Alevras, UCSB
  • Title: The standard form of an E₀-semigroup, Part I
  • Abstract:
    I will give an update on some fairly recent developments on the
    classification problem of one-parameter semigroups of endomorphisms of
    B(H).
• Date: 4/6/01 (Friday)
  • Speaker: Anne Louise Svendsen, UCSB
  • Title: On Invariants for Subfactors
• Date: 4/12/01 (Thursday)
  • Speaker: Alexis Alevras, UCSB
  • Title: The standard form of an E₀-semigroup, Part II
• Date: 4/13/01 (Friday). Different room and time! Time: 2-3pm, Room: SH 4607
  • Speaker: Jorgen Andersen, Aarhus University
  • Title: The Gauge Theory Construction of TQFT’s and the Asymptotic
    Expansion Conjecture
    
  • Abstract: I shall provide some details of the topics discussed in
    yesterday’s colloquium talk. In particuluar, I shall explain the asymptotic
    expansion conjecture,
    which is concerned with the semi-classical limit of the partition
    functions (or quantum invariants) associated to a TQFT. This is a
    mathematically well formulated
    conjecture, but it is motivated by a Feynman type expansion of the path
    integral expression of the partition function in a parameter, which plays
    the role of one over Planck’s constant. From its formulation, it is
    clear that this conjecture implies strong relations between these
    quantum invariants and the classical algebraic topology of
    3-manifolds such as Chern-Simons values on flat connections and
    the first fundamental group. Finally I shall present a proof of
    the conjecture for the class of 3-manifolds which are mapping
    cylinders of finite order diffeomorphims of 2-dimensional
    surfaces. This proof uses the Lefschetz-Riemann-Roch theorem on
    a singular algebraic variety and the moduli space of semi-stable
    bundles on a Riemann surface, of which the diffeomorphism is an
    automorphism.
• Date: 4/20/01 (Friday)
  • Speaker: Joachim Cuntz, University of Muenster
  • Title: Non-commutative simplicial complexes and the Baum-Connes conjecture
• Date: 4/27/01 (Friday)
  • Speaker: Florian Vasilescu, University of Lille
  • Title: Invariant subspaces for some families of unbounded
    subnormal operators
  • Abstract:
    We exploit the resources of Thomson’s and Trent’s
    techniques, in particular the use of Cauchy type transforms
    for certain measures, to obtain some information concerning
    the existence of proper invariant subspaces for specific
    families of unbounded subnormal operators.
• Date: 5/3/01 (Thursday)
  • Speaker: Hans Wenzl, UC San Diego
  • Title: Categorical Constructions for Subfactors
• Date: 5/4/01 (Friday)
  • Speaker: Eberhard Kirchberg, Humboldt University Berlin
  • Title: Classification of non-simple purely infinite algebras
• Date: 5/10/01 (Thursday)
  • Speaker: Nate Brown, MSRI
  • Title: On Connes’ embedding conjecture
• Date: 5/11/01 (Friday)
  • Speaker: Dimitri Shlyakhtenko, UCLA and MSRI
  • Title: Free Araki-Woods factors
  • Abstract:
    Free Araki-Woods factors are free-probability analogs of
    classical Araki-Woods factors (these are hyperfinite von Neumann
    algebras, typically type III factors). The main open problem is to give
    a classification of free Araki-Woods factors. In our previous work, we
    completely solved this classification question for free Araki-Woods
    factors having almost-periodic states. Using Connes’ invariant tau, we
    show that there is a continuum of mutually non-isomorphic free
    Araki-Woods factors with no almost-periodic states (this is in contrast
    to the hyperfinite situtation). We introduce a further invariant of a
    type III factor, and use it to distinguish two non-isomorphic free
    Araki-Woods factors, having the same tau invariant.
• Date: 5/17/01 (Thursday)
  • Speaker: Marius Dadarlat, Purdue University and MSRI
  • Title: On groups uniformly embeddable in a Hilbert space
• Date: 5/18/01 (Friday), 11 am at ITP (different place and time!)
  • Speaker: Alain Connes, IHES and MSRI
  • Title: Noncommutative Geometry
• Date: 5/18/01 (Friday)
  • Speaker: George Elliott, University of Toronto
  • Title: Recent progress in the classification of amenable C*-algebras
• Date: 5/24/01 (Thursday)
  • Speaker: Mikael Rørdam, University of Copenhagen (visiting UCSB)
  • Title: A simple C*-algebra with a finite and infinite projection
    
• Date: 5/25/01 (Friday)
  • Speaker: Ken Dykema, Texas A&M University
  • Title: Decomposability of DT-operators
  • Abstract:
    Operators modeled on certain upper triangular random matrices
    are called DT-operators, and this class includes Voiculescu’s circular
    operator. We show that DT-operators are decomposable in the sense of
    Apostol and Foias. Even more, a DT-operator has a family of invariant
    subspaces parametrized on the Borel subsets of its spectrum, which
    decompose the operator in a well described way.
    
• Date: 6/1/01 (Friday)
  • Speaker: Mikael Rørdam, University of Copenhagen (visiting UCSB)
  • Title: Classification of infinite simple C*-algebras