Operator Algebras Seminar, Fall 1996

• Date: 10/4/96
  • Speaker: Chuck Akemann, UCSB
  • Title: Lyapunov's Theorem meets the Spectral Theorem in a II_1 factor?

• Date: 10/10/96, Math Colloquium
  • Speaker: Dan Voiculescu, UC Berkeley
  • Title: Free Probability Theory and von Neumann Algebras
  • Abstract: In noncommutative probability theory independence can be based on free products instead of tensor products . This leads to a highly noncommutative theory: freely independent variables do not commute in general. Convolution operators on free groups and random matrices in the large N limit provide models for free independence . The theory has led to the solution of several problems concerning the von Neumann algebras of free groups.

• Date: 10/18/96
  • Speaker: Eero Saksman, University of Helsinki
  • Title: Multipliers on spaces of bounded linear operators

• Date: 10/25/96
  • Speaker: Bjorn Birnir, UCSB
  • Title: Well-posedness

• Date: 11/1/96
  • Speaker: Dietmar Bisch, UCSB
  • Title: Introduction to subfactors, Part I: commuting squares

• Date: 11/8/96
  • Speaker: Tony Falcone, UCLA
  • Title: A Canonical Construction for the Core of a Type III von Neumann A lgebra
  • Abstract: It has long been a part of the ``folklore'' associated with the theory of Type III von Neumann algebras that the (Type II_\infty) core which arises in the crossed product decompostion of an arbitrary Type III von Neumann algebra M is, in fact, a canonical object. That is to say, it should not depend on the choice of (faithful, normal and semi-finite) weight \phi. Of course, typically one would denote the core N of M by M \rtimes_{\sigma^\phi}R, which indicates the dependence of N on the choice of phi. It is possible, however, to construct N in such a way that it no longer depends on one's choice of weight.

• Date: 11/15/96, 3:30 pm (note: different time)
  • Speaker: Hans Wenzl, UCSD
  • Title: Subfactors from quantum groups at roots of unity

• Date: 11/21/96
• Mathematics Colloquium, SH 6635
  • Speaker: Dietmar Bisch, UCSB
  • Title: A survey of subfactors
  • Abstract: The analysis of subfactors, i.e. certain inclusion of algebras of operators on a Hilbert space, led Vaughan Jones in the early 80's to the discovery of his knot invariant, the Jones polynomial. A subfactor has a rich analytical and combinatorial structure and we will illustrate some of the combinatorial aspects in detail. In particular, certain bipartite graphs appear as basic invariants associated to subfactors, including the Coxeter-Dynkin graphs of type A, D_{2n}, E_6 and E_8. Extremely rigid systems of inclusions of finite dimensional algebras arise naturally from the representation theory of a subfactor such as the system of Temperley-Lieb algebras, which turns out to be the fundamental symmetry associated to every subfactor. We will try to explain in this talk the basic objects and some of the fundamental concepts appearing in the theory of subfactors and we will discuss the interactions of the theory of subfactors with theoretical physics and other fields of mathematics, such as low dimensional topology.

• Date: 11/22/96
  • Speaker: Stephen Simons, UCSB
  • Title: On finite familes of convex functions on a convex set

• Date: 11/29/96
  • no meeting (Thanksgiving Holiday)

• Date: 12/6/96
  • Speaker: Mohammed Dahleh, UCSB (Engineering)
  • Title: The Formulation of a Class of Robust Control Design Questions as Problems in Functional Analysis