Operator Algebras Seminar, Spring 2001

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
    

• Past Operator Algebras Seminars