September 22nd:

Rufus Willett (Vanderbilt), A survey of property (T) and Kazhdan projections

I will give a brief overview of the effects of property (T) on the unitary dual of a (discrete, residually finite) group, e.g. SL(3,Z), and how this leads to the existence of lots of projections in the full group C*-algebra, so-called 'Kazhdan projections'.  I will then give an (again, brief!) account of work of Vincent Lafforgue that directly proves the existence of generalised Kazhdan projections, and some consequences for actions on, and embeddings into, uniformly convex Banach spaces.  There won't be any genuinely new results, and the talk should be accessible to graduate students.

September 29th:

Rufus Willett (Vanderbilt), Construction of Kazhdan projections after Vincent Lafforgue

I will continue roughly where I left off last time: I will start by discussing concrete estimates for decay of matrix coefficients on SL(3,R), and how this leads to constructions the Kazhdan projection.  I will then discuss Lafforgue's approach to proving similar estimates for matrix coefficients of SL(3,Q_2) in uniformly convex Banach spaces; a central point is that the combinatorial geometry of cubes cannot be reproduced in a uniformly convex space, and that such cubes are modelled by 2-adic integers.

October 6th:

Dongping Zhuang (Vanderbilt), Property A for mapping class groups I

I'll talk about Yoshikata Kida's proof of property A for mapping class groups.  The proof is included in the seminal paper: The mapping class group from the viewpoint of measure equivalent theory. Since I'm not an expert in either field, this will be an informal talk, and the main purpose of this study is to see if this proof will give us some hint to the case of other groups, like the outer automorphism groups of free groups.

October 13th:

Dongping Zhuang (Vanderbilt), Property A for mapping class groups II

I'll talk about Yoshikata Kida's proof of property A for mapping class groups.  The proof is included in the seminal paper: The mapping class group from the viewpoint of measure equivalent theory. Since I'm not an expert in either field, this will be an informal talk, and the main purpose of this study is to see if this proof will give us some hint to the case of other groups, like the outer automorphism groups of free groups.

October 20th:

Joint with colloquium, so in SC 5211

Cornel Pasnicu (University of Puerto Rico), Noncommutative zero dimensional topological spaces.

A C*-algebra can be thought as a noncommutative topological space or as a collection of infinite matrices of complex numbers endowed with an interesting algebraic and topological structure. The C*-algebras have significant applications in different areas of mathematics (geometry, topology, ergodic theory), parts of physics (quantum mechanics and statistical mechanics) and other sciences. Understanding the structure and classification of C*-algebras was and continues to be one of the most important researh directions in Operator Algebras (Elliott and Kirchberg, I.C.M. 1994, Rordam, I.C.M. 2006). In this talk I will present, in a natural context and giving basic definitions and examples, a joint work with Mikael Rordam (J. Reine Angew. Math. 2007) in which we characterize, in the separable case, for a large and important class of C*-algebras that are "infinite" in some specific sense (introduced 10 years ago by Kirchberg and Rordam) a certain condition of noncommutative zero dimensionality (introduced by Brown and Pedersen) that proved to be very successful in Elliott's well known Classification Program for C*-algebras (I.C.M. 1994). (It is perhaps worth to mention also that many C*-algebras of interest happen-sometimes surprisingly-to satisfy this condition). Some interesting consequences of this result that concern the structure of C*-algebras will be also discussed. Our theorem strongly generalizes a result of Perera and Rordam (J. Funct. Anal. 2004) and, in the separable case, a result of Zhang.

October 27th:

Hanfeng Li (University at Buffalo, SUNY), Hilbert C*-modules not embeddable as direct summands of standard modules

Abstract: It is a direct consequence of Kasparov's stabilization theorem that every countably generated Hilbert C*-module is a direct summand of the standard Hilbert C*-module over an infinite countable base. Using the notion of frame, I will show that there are Hilbert C*-modules which can not be embedded as a direct summand of any standard Hilbert C*-module over any base.

November 3rd:

Denis Osin (Vanderbilt), Asymptotic dimension and type functions of finitely generated groups.

To each metric space of finite asymptotic dimension, one associates a collection of invariants called type functions. These functions are closely related to Hilbert space compression rate, dimension of asymptotic cones, and other asymptotic invariants.  I will review some results about type functions of connected Lie groups, lattices, and relatively hyperbolic groups. We will also discuss the question which functions can be realized as type functions of finitely generated groups.

November 10th:

Marius Junge (University of Illinois Urbana-Champaign), Operator algebra techniques in Quantum information

By now there are a number of connections between operator algebras and Quantum Information Theory (QI) beside the obvious one that completely positive maps are important in both areas. In this talk I will focus on violations of Bell inequalities for tripartite and bipartite systems, and show how free groups, free probability, and, of course, tensor norm techniques from operator space yield (almost) optimal bounds and examples for violations.
(Joint work with Perez-Garcia, Villuneavo, Wolf, Villuneavo and Palazuelos)

November 17th:

Mrinal Raghupathi (Vanderbilt), Toeplitz corona theorems for some algebras of holomorphic functions
(joint with Brett D. Wick)

In this talk I will describe the operator theoretic version of the classical corona problem. I will explain the connection to the tangential version of the Nevanlinna-Pick interpolation problem and an associated distance problem.

I will show how the well-known distance-duality method can be used to prove a new Toeplitz corona theorem for Riemann surfaces and also recover known results on the ball, polydisk, and Drury-Arveson space.

December 1st:

Romain Tessera (CNRS), A geometric decomposition property for linear groups.

In a joint work with Erik Guentner and Guoliang Yu, we prove that any countable subgroup of the linear group over a field K has "finite decomposition complexity". As a result, we obtain a topological rigidity property for any closed aspherical manifold whose fundamental group is linear.

December 8th: No seminar.