Quantum Statistical Mechanics of $\mathbb{Q}$-lattices and noncommutative geometry

Abstract

After recalling some basic notions of quantum statistical mechanics, we explain the Bost-Connes system that relates the structure of the maximal abelian extension of $\mathbb{Q}$ to the space of \kms states of a \cs-dynamical system. Afterwards, we study briefly the Connes-Marcolli ${\text{GL}}_2$-system as a generalization of the former system.

These are (updated version of) my notes of the talk given as the second part of the author comprehensive examination at the University of Western Ontario in May 2005. Some recent developments have been considered and some new references have been added. (10 pages)

References in corpus (1)

• The Regular C*-algebra of an Integral Domain