Seminar in operator theory and operator algebras (MATH 9310)
Fall 2015

The seminar is organized by David Sherman. We meet Tuesdays 4-5 in Kerchof 326.

September 8

Kristin Courtney, UVa

The full C*-algebra of the free group on two generators

This talk will center around the similarly titled paper by Man-Duen Choi (appearing in print in 1980). I will provide a brief description of the full group C*-algebra for a locally compact Hausdorff group as well as a useful characterization for the full group C*-algebra for the free group on two generators in terms of universal pairs of unitaries. We will see why this C*-algebra with abundant ideals is, in fact, a primitive C*-algebra with no nontrivial projections, which can also be faithfully represented as a *-subalgebra of a countable direct sum of finite-dimensional matrix algebras.

September 15

No meeting

September 22

Craig Kleski, Miami University (Ohio)

Classifying C*-algebras generated by representations of nilpotent groups

Group C*-algebras come in many flavors, with few general results known about their structure. In this talk, I explain how to classify C*-algebras generated by faithful irreducible representations of the unitriangular group UT(4,Z). In principle, this allows for an explicit decomposition of the C*-algebra as an inductive limit of tractable C*-algebras and thus reveals much information. I will review relevant parts of K-theory for C*-algebras and the Elliott program, and try to convince you why you should care about UT(4,Z). This is joint work with Caleb Eckhardt and Paul McKenney.

September 29

Kristin Courtney, UVa

The full C*-algebra of the free group on two generators

Continuation from September 8.

October 6

Reading day (no meeting)

October 13

Kevin Beanland, Washington and Lee University

Classes of operators determined by ordinal indices

We will discuss some newly discovered closed two-sided operator ideals that are defined using ordinals. The classes of operators are defined using a generalization of Bourgain's tree index. The is joint work with Ryan Causey, Dan Freeman and Ben Wallis.

October 20

Chris Ramsey, UVa

C*-algebras isomorphic after tensoring with Mn

In 1977 Joan Plastiras gave a striking example of two non *-isomorphic C*-algebras A and B such that M2(A) and M2(B) are isomorphic. But what happens when we amp up this question? If Mn(A) and Mn(B) are isomorphic for every n > 1 does this imply that A and B are isomorphic? The answer, care of a plucky Dane, is quite delightful and will lead us on a merry jaunt through some interesting theory.

October 27

Ali Kavruk, Virginia Commonwealth University

Relative weak injectivity for C*-algebras

Extending C. Lance`s weak expectation property, E. Kirchberg introduced the notion of relative weak injectivity for arbitrary pairs of C*-algebras. In this presentation we focus on non-commutative versions of several order theoretic concepts such as tight Riesz interpolation and decomposition properties and Arveson-Riesz extension properties with their connection to relative weak injectivity. We exhibit several examples of these notions in the category of Kadison and Banach spaces, which in turn, yield characterizations for simplicial and Lindenstrauss spaces. We discuss several formulations of Connes` embedding problem via Arveson-Riesz extension properties. For general operator systems, by extending some of the result of E. Effros, we formulate function theoretic characterization of (c,max) nuclearity, which distinguishes the C*-systems among the others. Time permitting, we will discuss weak rigidity for operator systems, a joint work with C. Kleski.

November 3

Isabelle Chalendar, Université Lyon I

On the compactness of truncated Toeplitz operators

Truncated Toeplitz operators are the compressions of Toeplitz operators on model spaces. In a joint work with E. Fricain and D. Timotin, we investigate the property of compactness for these operators through natural embedding measures associated with these operators.

Nate Brown (Penn State) will give the department colloquium on November 5.
VOTCAM will be held at Washington & Lee University on November 7.

November 10

No seminar

November 17

Elias Katsoulis, East Carolina University

Crossed product constructions in operator algebra theory

November 24

No seminar... last work hour before Thanksgiving break.

December 1

No seminar. There will be an analysis lecture series by Stuart White (University of Glasgow) probably December 3-4.

You can reminisce about previous semesters at the links below:
Spring 2015 Fall 2014 Spring 2014 Fall 2013 Spring 2013 Fall 2012 Spring 2012 Fall 2011 Spring 2011 Fall 2010 Spring 2010 Fall 2009 Spring 2009 Fall 2008 Spring 2008 Fall 2007 Spring 2007 Fall 2006 Spring 2006 Fall 2005 Spring 2005 Fall 2004 Spring 2004 Fall 2003 Spring 2003 Fall 2002