• Date: 8/26/16
  • Scott Atkinson, Vanderbilt University.
  • Title: Minimal Faces and Schur's Lemma for Embeddings into R^U.
  • Abstract: In this talk, we will see a generalization of N. Brown's characterization of extreme points in Hom(N,R^U). In particular, given a separably acting II_1-factor N and an ultrapower of the separably acting hyperfinite II_1-factor R^U, we will show that given \pi: N \rightarrow R^U, the dimension of the minimal face containing [\pi] is one less than the dimension of the center of the relative commutant of \pi. A consequence of this is the "convex independence" of extreme points: the convex hull of n extreme points is an n-vertex simplex. Along the way, we will establish a version of Schur's Lemma in this context.

• Date: 9/2/16
  • Arnaud Brothier, Vanderbilt University.
  • Title: Hyperfinite realizations of abstract standard invariants
  • Abstract: To any subfactor can be associated a combinatorial object called the standard invariant. This combinatorial object can be defined abstractly. By Popa's reconstruction theorem, any abstract standard invariant comes from a subfactor. But it is an open question to know if any standard invariant can be realized by a hyperfinite subfactor. I will discuss about hyperfinite realizations of abstract standard invariants and present new results on this matter.

• Date: 9/9/16

• Date: 9/16/16
  • Ian Charlesworth, UCLA
  • Title: Free Entropy and Polynomials
  • Abstract: Free entropy has been a topic of study since it was introduced by Voiculescu in the 1990's. It can be seen as giving certain regularity conditions on the joint distributions of non-commuting random variables. I will discuss consequences of such regularity assumptions on a set of variables to the algebra of polynomials they generate. Time permitting, I will also introduce an approach to entropy in the bi-free setting.

• Date: 9/23/16
  • Vaughan Jones, Vanderbilt University
  • Title: An update on those unitary representations of Thompson groups.
  • Abstract: We will recall the definition of the Thompson groups as groups of fractions of categories of forests and how that was used to obtain representations from planar algebras. Then we will use simpler data to obtain "classical" analogues where the tensor product is replaced by the direct sum. The upshot will be the existence of a unitary representation of $F$ for every solution $(A,B)$ of the operator equation $|A|^2+|B|^2=1$ on Hilbert space. We will look at these representations for some of the simplest solutions to this equation.

• Date: 9/30/16

• Date: 10/7/16
  • Sandeepan Parekh, Vanderbilt University
  • Title: Maximal amenability of the generator masa in q-Gaussian factors.
  • Abstract: For -1 < q < 1, Bozejko and Speicher's q-Gaussian factors can be thought of as q-deformed versions of the free group factor. Indeed they are known to share several properties in common with the free group factors like being non-injective, strongly solid, isomorphic to LF_n (for |q| small enough). Continuing this line of investigation, in a joint work with K. Shimada and C. Wen, we show the generator masa in these factors are maximal amenable.

• Date: 10/14/16
  • No Meeting, Fall Break.

• Date: 10/21/16
  • Brent Nelson, UC Berkeley

• Date: 10/28/16
  • Craig Kleski, Miami Univerity in Ohio

• Date: 11/4/16
  • Hung-Chang Liao, Penn State University

• Date: 11/11/16
  • Daniel Drimbe, UC San Diego

• Date: 11/18/16

• Date: 11/25/15
  • No Meeting, Thanksgiving Break.

• Date: 12/2/16

• Date: 12/9/16

• End of Fall Semester.

Past NCGOA and Subfactor seminars