Dynamics and C*-Algebras: Amenability and Soficity (14w5161)


(University of Toronto)

(University of Ottawa)

(Texas A&M University)

Andrew Toms (Purdue University)


The Banff International Research Station will host the "Dynamics and C*-Algebras: Amenability and Soficity" workshop from October 19th to October 24th, 2014.

Conceived by von Neumann in the 1920s as a foundation for quantum physics
and the mathematics of continuous dimensionality, the theory of operator algebras has developed in
large part through ideas of a dynamical nature and has enjoyed a rich variety of connections
to the study of group actions. Topological dynamics has in particular played a significant role
in the theory of C*-algebras by providing a tool for the coordinatization of algebraic structure.
Progress over the last several years at the interface of C*-algebra classification theory and dynamics
has generated a host of tantalizing conceptual and technical questions involving
regularity properties of C*-algebras, dimensional versions of entropy, noncommutative dimension theory,
Rokhlin tower decompositions, perforation, orbit equivalence, and amenability. The workshop will
pursue these lines of investigation in a way that integrates the expertise of specialists in dynamical systems
who may not be versed in C*-classification theory. This is especially timely as recent developments
in C*-classification have honed on issues that have long been central in dynamics,
such as the tension between additive and multiplicative structure that is characteristic of amenability
and the distinction between internal and external approximation that figures prominently
in the currently very active study of sofic groups.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).