Operator algebras and dynamical systems from number theory (13w5152)


(Australian National University)

Marcelo Laca (University of Victoria)


The Banff International Research Station will host the "Operator algebras and dynamical systems from number theory (HALF)" workshop from November 24th to November 29th, 2013.

The topic of the workshop lies within the interface between two areas: Operator Algebras (and Noncommutative Geometry),
which contribute the techniques and motivations developed for quantum physics, and Number Theory as a source of problems
and constructions on which to apply these techniques.

The idea that the theory of operators on Hilbert space can be used to shed light onto long standing problems in number theory
goes back at least as far as Polya and Hilbert himself. Recently, however, there has been a rekindling of the interest on this approach
under a very promising new shape. This renewal first arose from the pursuit of physical analogies in number theory, but it owes
its current significant momentum to the pioneering vision of Alain Connes. The program consists of constructing noncommutative
dynamical systems based on number theoretic data. These dynamical systems are essentially non-physical, as they originate from
abstract constructions from number theory, but their study following the principles and methods of quantum statistical mechanics
yields a fascinating interplay between ideas from quantum physics and constructions from number theory. A running theme of this
interplay is the study of equilibrium and the associated symmetries, which play a prominent role both in physics and in number theory.

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).