(Sub)factor Seminar

Fall 2008

Fridays, 4:10-5:30pm in SC 1310

• Date: 8/25/08
  • Organizational meeting.

• Date: 9/5/08
  • no meeting, Wabash Modern Analysis Seminar

• Date: 9/12/08
  • Romain Tessera, Vanderbilt University
  • Title: A characterization of relative property T (joint work with Yves de
    Cornulier)
  • Abstract:
    We prove that a semidirect product of a group G with an abelian
    group V does not have relative property T with respect to V if and only if
    there exists a mean on the dual of V, which is
    
    -G-invariant,
    
    -supported on the trivial representation,
    
    -distinct from the dirac measure.

• Date: 9/19/08
  • Pinhas Grossman, Vanderbilt University
  • Title: Strong Singularity for Subfactors
  • Abstract:
    We will describe an example of a subfactor of the
    hyperfinite II₁ factor which is singular but not strongly singular
    (with constant one). This is joint work with Alan Wiggins.

• Date: 9/26/08
  • Thomas Sinclair, Vanderbilt University
  • Title: Superrigidity of Bernoulli Actions of Some Product Groups
  • Abstract:
    Following Sorin Popa (“On the Superrigidity of Malleable
    Actions with Spectral Gap,” available on arXiv) I will demonstrate that
    the Bernoulli action of G = H x K is cocycle superrigid, where H is a
    nonamenable group and K is an arbitrary infinite group. As a consequence,
    any group L which has an ergodic action orbit equivalent to the Bernoulli
    action of G is isomorphic to G and the actions are conjugate.

• Date: 10/3/08
  • Shamindra Ghosh, Vanderbilt University
  • Title: From planar algebras to subfactors
  • Abstract:
    Starting from a planar algebra satisfying suitable conditions,
    we will describe the construction (by Jones, Shlyakhtenko and Walker) of
    a subfactor whose planar algebra is the one with which we started. The
    first construction was given by Popa, and then by Guionnet, Shlykhtenko
    and Jones.

• Date: 10/10/08
  • Jesse Peterson, Vanderbilt University
  • Title: Derivations and quantum Dirichlet forms on von Neumann algebras, an introduction.
  • Abstract: We will give in introductory talk to the theory of
    derivations and quantum Dirichlet forms on von Neumann algebras.
    Emphasis will be placed on the association between closable real
    derivations, closable quantum Dirichlet forms, and semigroups
    of completely positive maps, à la Jean-Luc Sauvageot. We will then
    describe how this association can be applied to various situations
    such as those involving group and group-measure space von Neumann
    algebras.

• Date: 10/17/08
  • Junhao Shen, University of New Hampshire
  • Title: Topological Free Entropy Dimension for Blackadar and Kirchberg’s MF algebras.
  • Abstract: We will start the talk with introduction to MF C*-algebras
    in the sense of Blackadar and Kirchberg. Then we will indicate the
    connection between MF C*-algebras and Brown-Douglas-Fillmore’s
    extension semigroup. Basing on the work by Haagerup and Thorbjornsen
    on the reduced group C*-algebras of free groups, we will give
    several new examples of Blackadar and Kirchberg’s MF algebras,
    followed by several new examples of C*-algebras whose BDF-extension
    semigroup is not group.

    In the second half of the lecture, we will introduce Voiculescu’s
    topological free entropy theory for unital C*-algebras. We will see
    the reason why the definition of Voiculescu’s free entropy is based
    on the properties of MF C*-algebras. Then we will present some
    calculation of topological free entropy dimension for several
    important classes of MF C*-algebras.

• Date: 10/24/08
  • Junsheng Fang, Texas A&M University
  • Title: The radial (Laplacian) masa in a free group factor is maximal injective
  • Abstract:
    The radial (or Laplacian) masa in a free group factor is the
    abelian von Neumann algebra generated by the sum of the generators (of
    the free group) and their inverses. We prove that the Laplacian masa
    has an asymptotic orthogonality property and therefore is maximal
    injective in the free group factor. Combining with Popa’s intertwining
    technique and our recent results of groupoid normalizers of tensor
    product von Neumann algebras, we are able to prove that the tensor
    product of a type I maximal injective von Neumann subalgebra which has
    the asymptotic orthogonality property with an arbitrary type I
    maximal injective von Neumann sublagebra is maximal injective. This is
    joint work with Jan Cameron, Mohan Ravichandran and Stuart White.

• Date: 10/31/08
  • no meeting, Von Neumann Algebras and Ergodic Theory of Group Actions

• Date: 11/7/08
  • Shamindra Ghosh, Vanderbilt University
  • Title: From planar algebras to subfactors, Part II
  • Abstract:
    Starting from a planar algebra satisfying suitable conditions,
    we will describe the construction (by Jones, Shlyakhtenko and Walker) of
    a subfactor whose planar algebra is the one with which we started. The
    first construction was given by Popa, and then by Guionnet, Shlykhtenko
    and Jones.

• Date: 11/14/08
  • Alan Wiggins, Vanderbilt University
  • Title: Groupoid Normalizers of Tensor Products
  • Abstract:
    Given a unital subalgebra B of a II_1 factor M , define the groupoid
    normalizers
    G_N(B) of B in M to be all partial isometries v \in M with vBv* , v*Bv
    \subset B. We show that when B_i’ \cap M_i = Z (B_i), i = 1, 2, then
    G_N(B_1)” \otimes G_N(B_2)” = G_N(B_1 \otimes B_2)” .
    This is joint work with Roger Smith, Stuart White, and Junsheng Fang.
    
    pdf version

• Date: 11/21/08
  • Ionut Chifan, UC Los Angeles
  • Title: Deformation/spectral gap rigidity principle for von Neumann algebras and some applications to ergodic theory
  • Abstract:
    In this talk I will discuss Popa’s deformation/spectral gap rigidity technique for von
    Neumann algebras and I will present some new applications to solidity and to ergodic
    theory. For instance, I will prove the folowing result: Suppose that G \curvearrowright [0,1]^G is the
    Bernoulli action of a countable infinite group G and denote by
    R_{G \curvearrowright [0,1]^G} the induced equivalence relation. Then for every subequivalence relation
    S \subset R_{G \curvearrowright [0,1]^G} there exists a measurable partition {X_i}, i \geq 0 of [0,1]^G
    formed of R-invariant sets such that R_{|X_0} is
    hyperfinite and R_{|X_i} is strongly ergodic (hence non-hyperfinite and ergodic) for every i \geq 1.
    This talk is based on two papers I have written jointly with A. Ioana respectively C. Houdayer.

    pdf version

• Date: 11/28/08
  • no meeting, Thanksgiving break

• Date: 12/5/08
  • No meeting.

  Winter Break.