# Equilibrium states in semigroup theory, K-theory and number theory

Master class

The master class is a part of the project "Pure Mathematics in Norway, 2018-2022", supported by the Trond Mohn Foundation and the Tromsø Research Foundation.

During the past 25 years there has been a significant activity constructing and analyzing C*-algebras and C*-algebraic dynamical systems from semigroups of number theoretic origin. Among these are the semigroup C*-algebras of the affine semigroup of the ring of algebraic integers in a number field, which are closely related to the Bost-Connes systems giving a thermodynamic interpretation of the Riemann and Dirichlet zeta-functions. The K-theory of the associated boundary quotients has been computed and also the phase transition of equilibrium states at low temperature has been exhibited via a natural parametrization. There is an intriguing, and still not understood, parallel in that the same C*-algebra lies at the heart of the solution of both problems. The goal of the master class is to introduce the participants to these and related topics lying at the intersection of several branches of mathematics.

The main program will consist of three series of lectures given by

- Marcelo Laca
- Xin Li
- Alina Vdovina

The detailed program is available here. The lectures will take place at the main campus of the University of Oslo, in two buildings - Niels Henrik Abels hus (mathematics institute) and Georg Sverdrups hus (main library). Here is some practical information from a previous master class how to get there.

Slides/notes of some of the talks: Laca, Li, Vdovina, Christensen, Tao