Operator Algebras Seminar, Fall 1998

• Date: 9/30/98
  • Dietmar Bisch, UCSB
  • Title: An abstract characterization of the standard invariant of a subfactor (after Popa), Part I

• Date: 10/7/98
  • Speaker: Dietmar Bisch, UCSB
  • Title: An abstract characterization of the standard invariant of a subfactor (after Popa), Part II

• Date: 10/14/98
  • no meeting

• Date: 10/21/98
  • Speaker: Anne Louise Svendsen, UCSB
  • Title: The principal graphs of a subfactor

• Date: 10/28/98
  • Speaker: Chuck Akemann, UCSB
  • Title: Geometric Spectral Theory
  • Abstract: I'll start with a brief review of spectral theory for (bounded) self-adjoint operators; then I'll explain how one can get a geometric view of the spectrum of a single operator. When we move to more than one operator, we need to assume that the operators live in a II_1 factor. When we do so, the geometric approach that worked for one operator can be extended to any finite number of self-adjoint operators. The geometric objects constructed are convex sets in R^n, and convexity plays a large role in the proofs. (This talk can be viewed as an advertisement for my 260 course on convexity in Winter Quarter.)

• Date: 11/5/98, Mathematics Colloquium, SH 6635, 3:30-4:30pm
  • Speaker: Erling Stormer, University of Oslo
  • Title: Noncommutative entropy
  • Abstract: The concept of entropy plays an important role in physics, information theory and ergodic theory. In ergodic theory it appears as an important invariant for measure preserving transformations between measure spaces and Kolmogoroff and Sinai used entropy to show that certain Bernoulli shifts are not isomorphic.
    There are several extensions of the notion of entropy to the noncommutative setting, which apply in particular to the analysis of automorphism of operator algebras. We will give a survey of some of these ideas with special emphasis on showing how results from the theory of entropy give information about various problems in operator algebras.

• Date: 11/6/98, FA seminar, SH 6635, 4:00-6:00pm (note: different date!)
  • Speaker: Erling Stormer, University of Oslo
  • Title: Generators for entropy in finite von Neumann algebras
  • Abstract: This talk will be a continuation and specialization of the colloquium talk. I'll concentrate on the theory of generators - generalizing the corresponing concept in the classical case - and discuss the relationship to bitstreams and index of subfactors.

• Date: 11/11/98
  • Speaker: Ken Goodearl, UCSB
  • Title: Algebraic methods in real rank zero

• Date: 11/18/98
  • Speaker: Anne Louise Svendsen, UCSB
  • Title: Commutators associated to a subfactor (after Huang)

• Date: 11/25/98
  • no meeting (Thanksgiving Holiday)

• Date: 12/4/98, FA seminar, SH 6635, 4:00-6:00pm (note: different date!)
  • Speaker: V.S. Sunder, Institute of Mathematical Sciences, Madras
  • Title: The subgroup subfactor
  • Abstract: In a search for a `relative version' of Dye's theorem (on orbit equivalence of measure-preserving automorphisms of a Lebesgue probability space), Klaus Thomsen asked the following question: does the subfactor $(P \times H) \subset (P \times G)$ - where $P \times G$ denotes the crossed-product of a $II_1$ factor $P$ by a finite group $G$ acting as `outer automorphisms' of $P$, and $H$ denotes a subgroup of $G$ - remember the inclusion $H \subset G$ of groups.
    
    This talk will focus on the proof of the negative answer to this question, by discussing our `counter-example'; the fact that it is a counter-example rests on Popa's theorem on the `completeness of the standard invariant' (in the hyperfinite case), and on our explicit computation of the standard invariant for the subgroup subfactor.
    
    The only prerequisites for understanding the talk are familiarity with the basic theory of unitary representations of finite groups, and a minimal mathematical maturity.