Dynamics and C*-algebras: amenability and soficity
ABSTRACTS
Marius Dadarlat, Purdue University
K-theoretic quasidiagonality and almost flat bundles
We will discuss connections between K-theoretic quasidiagonality and the K-theoretic MF property of group C*-algebras C*(G), and the existence of nontrivial almost flat bundles on the classifying space of G.
Caleb Eckhardt, Miami University
Nilpotent group C*-algebras and nuclear dimension
We'll discuss a recent result (with P. McKenney) showing that finitely generated nilpotent group C*-algebras have finite nuclear dimension and some implications for Elliott's classification program.
Ruy Exel, Universidade Federal de Santa Catarina
The tight groupoid of an inverse semigroup
The main object of study in this talk will be the tight C*-algebra associated to an inverse semigroup. The C*-algebras arising from this construction are quite general, including all Kirchberg C*-algebras in the UCT. It is therefore interesting to relate algebraic properties of a given inverse semigroup S with those of its tight C*-algebra, including the tight groupoid of S, from which the tight C*-algebra may also be obtained. In this direction we will discuss properties of S which imply (or are equivalent to) that the tight groupoid is Hausdorff, essentially principal, minimal and contracting.
Matthew Kennedy, Carleton University
C*-simplicity and the unique trace property for discrete groups
In joint work with M. Kalantar, we established necessary and sufficient conditions for the simplicity of the reduced C*-algebra of a discrete group. More recently, in joint work with E. Breuillard, M. Kalantar and N. Ozawa, we proved that any tracial state on the reduced C*-algebra of a discrete group is supported on the amenable radical. Hence every C*-simple group has a unique tracial state. I will discuss these results, along with some applications.
Xin Li, Queen Mary, University of London
Amenability and the Liouville property
This talk is about amenability and the Liouville property. The goal is to explain these two notions and to discuss their relationship, for groups, groupoids, and semigroups.
Timothy Rainone, Texas A&M University
K-theoretical dynamics and finiteness in crossed products
We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. We describe K-theoretical conditions that give rise to RFD and MF reduced crossed products. In the presence of sufficiently many projections we associate to each noncommutative C*-system (A,G) notions of paradoxicality that characterize stably finite versus purely infinite crossed product algebras.
Leonel Robert, University of Lousiana at Lafayette
Commutators in pure C*-algebras
I will discuss my recent work, done jointly with Ping Wong Ng, on additive and multiplicative commutators in pure C*-algebras.
Yasuhiko Sato, Kyoto University
Elementary amenable groups are quasidiagonal
In 1987, J. Rosenberg proved that if the reduced group C*-algebra is quasidiagonal then the given group is amenable, and he conjectured that the converse also holds. We confirm this Rosenberg conjecture for elementary amenable groups. This is a joint work with N. Ozawa and M. Rørdam.
Adam Sierakowski, University of Wollongong
Filling families and strong pure infiniteness
I will talk about an refinement of a matrix diagonalization introduced by M. Rørdam and E. Kirchberg. As an application I will discuss how to verify strong pure infiniteness in various cases, including whether the minimal tensor product of a strongly purely infinite C*-algebra and an exact C *-algebra is again strongly purely infinite. This is join work with E. Kirchberg.
Karen Strung, Institute of Mathematics, Polish Academy of Sciences
A proof that the crossed products by minimal property (P) homeomorphisms of odd dimensional spheres are classified by their tracial state spaces
Abstract: Following up on Huaxin Lin's talk, I will give a detailed proof that the crossed products by minimal homeomorphisms of odd dimensional spheres are classified by their tracial state spaces for the special case that the homeomorphisms have "property (P)" as defined in Lin's talk. In particular, all known examples of nonuniquely ergodic minimal homeomorphisms have "property (P)".
Gabor Szabo, Westfälische Wilhelms-Universität Münster
Rokhlin dimension for actions of residually finite groups
In 2012, Ilan Hirshberg, Wilhelm Winter and Joachim Zacharias introduced the concept of Rokhlin dimension for actions of finite groups and the integers. Later this was adapted to actions of Zm. The main motivation for introducing this concept was that actions with finite Rokhlin dimension preserve the property of having finite nuclear dimension, when passing to the crossed product C*-algebra. Since then, this has been successfully used to verify finite nuclear dimension for a variety of non-trivial examples of C*-algebras, in particular transformation group C*-algebras. We extend the notion of Rokhlin dimension to cocycle actions of countable, residually finite groups. If the group in question has a box space of finite asymptotic dimension, then one gets an analogous permance property concerning finite nuclear dimension. We examine the case of topological actions and demonstrate a close connection between Rokhlin dimension and amenability dimension in the sense of Erik Guentner, Rufus Willett, and Guoliang Yu. As the main application, we show that free actions of finitely generated, nilpotent groups on finite dimensional spaces yield C*-dynamical systems with finite Rokhlin dimension, and hence their transformation group C*-algebras have finite nuclear dimension. This is joint work with Jianchao Wu and Joachim Zacharias.
Aaron Tikuisis, University of Aberdeen
Dimension and regularity for C*-algebras
One of the major recent themes in the structure of amenable C*-algebras concerns low-dimensional behaviour. There are a few candidate ways of measuring "low dimension" (called "regularity properties"), and conjecturally, they are equivalent under suitable, mild hypotheses. One particularly interesting regularity property, which I would like to highlight, involves noncommutative dimension theories, arising from a marriage of Lebesgue covering dimension and finite approximation properties (such as amenability). I will discuss these ideas and recent progress in this area.
Alessandro Vignati, York University
Amenable operator algebras and the isomorphism problem
We study the following question: is every amenable operator algebra isomorphic to a C*-algebra? Recently Choi, Farah and Ozawa provided a nonseparable counterexample, while Marcoux and Popov proved that any abelian amenable operator algebra is isomorphic to C0(X) for some locally compact X. In the first part of the talk we prove the existence of a nonseparable amenable operator algebra with additional properties. Secondly, we provide a criterion that is equivalent to "being isomorphic to a C*-algebra", and it is applicable in both the separable and nonseparable case.
Kun Wang, University of Toronto
On the bound of the C* exponential length and the classification invariants of C*-algebras
My talk contains two parts. In the first part, I will give an example in a simple inductive limit C*-algebra whose exponential length is close to 2π. As a consequence, combining with H. Lin's result, we know that 2π is an optimal bound of celCU(A) for unital separable simple C*-algebra A with tracial rank less and equal than 1. In part two, I want to show some classification results by using the Elliott's Invariant and Stevens' Invariant. And then I will show that these two invariants are equivalent when we consider the C*-algebra with the ideal property.
Qingyun Wang, University of Toronto
Regularity properties and actions with the weak tracial Rokhlin property
The tracial Rokhlin property was introduced by Chris Phillips to study the structure of the crossed product of actions on C*-algebras. It is more flexible than the Rokhlin property, and still yields important structural theorems. In this talk, we will generalize the definition of tracial Rokhlin property to actions of amenable groups and to C*-algebras possibly without projections, which we shall call the weak tracial Rokhlin property. We will show that the crossed product of an action with the weak tracial Rokhlin property preserves the following classes: (1) tracially Z-stable C*-algebras, and (2) C*-algebras whose Cuntz semigroup is almost unperforated and almost divisible. If time permits, we will also talk about some interesting examples. This is joint work with Chris Phillips and Joav Oravitz.