Equilibria on Toeplitz extensions of higher-rank noncommutative solenoids (25rit031)

The Banff International Research Station will host the “Equilibria on Toeplitz extensions of higher-rank noncommutative solenoids” workshop in Banff from February 9 - 16, 2025.

In quantum mechanics, a quantum statistical system is given by a C*-algebra (the collection of observables) and a time evolution modelled by a one-parameter group of automorphisms. An equilibrium state at an inverse temperature is a positive linear functional satisfying the KMS condition with respect to the time evolution, and describes the state of the system in thermal equilibrium. The analysis of KMS states naturally leads to very interesting (old and new) questions within pure mathematics, and they are vastly studied from this view-point.

The remarkable system constructed by Bost and Connes in the 90s was based on a Hecke algebra, which was later shown to arise from dynamics of semigroups by Laca and Raeburn. This realization simplified much of the analysis of phase transitions and KMS states in the original work of Bost and Connes. Since then C*-algebras associated with dynamics of semigroups have proved to exhibit a very interesting structure of KMS states and phase transitions. In this research project we will study the KMS state space and phase transitions for a class of C*-algebras associated with semigroups that occur as extensions of limits of higher-dimensional noncommutative tori.

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).