# Nadia Larsen: Phase transitions and arithmetic subalgebras for Hecke C*-algebras from number fields

**Time: **
Wed 2019-05-08 15.30

**Lecturer: **
Nadia Larsen (University of Oslo)

**Location: ** Room 32, building 5, Kräftriket, Department of Mathematics, Stockholm University ￼

In the mid 1990's J.-B. Bost and A. Connes introduced a C*-dynamical system having remarkable connections with number theory. The C*-algebra of the system is a completion of the Hecke algebra of a group-subgroup pair arising from the ring inclusion of the integers in the rationals, and the time evolution of the system emerges from the modular function

of the Hecke pair. The system admits a phase transition for equilibrium states and features an arithmetic subalgebra. The talk will concentrate on the main ingredients in the Bost-Connes construction and on a phase transition and arithmetic subalgebra in the context of arbitrary number fields obtained in joint work with M. Laca (Victoria) and S. Neshveyev

(Oslo).