# Operator algebra and dynamics

This network aims to connect the theory of operator algebra and the theory of dynamical systems. Despite difference between these two areas of mathematics, it turns out that they have a common generic structure, and that the study of the relation between them has been very fruitful. The basis for this relationship is different ways of associating C*-algebras to dynamical systems in a way such that the C*-algebras reflect the structure of the corresponding dynamical systems.

In recent years this correspondence between the two mathematical areas have evolved rapidly. Especially the classification of the two theories has turned out to be closely related and have manifested itself in an intensive exchange of methods, particularly as invariants. At present this subject is benefiting from a profound kinship which manifests itself as an intensive exchange of ideas. Among the concrete results are new invariants for dynamical systems and series of new examples of C*-algebras. An important example of the latter is the Cuntz-Krieger algebras, which in a natural way can be seen as C*algebras of shift of finite type, and a prime example of the former is the case of Cantor minimal systems which have been classified up to strong orbit equivalence through operator algebra by Skau et al.

Several research groups in Scandinavia belong to the world elite in operator algebra, and there is cooperation between these groups, in particular within applications of operator algebra to dynamics. The aim of this project is to formalise and strengthen this cooperation and establish the Nordic countries among the leading countries within the subject "operator algebra and dynamics". This will give PhD students and post-docs from the research groups an exceptional opportunity to get involved in collaboration with each other and with some of the leading experts within the subject.

The network supports students and researchers visiting other network groups, organises annual workshops, and serves as a Nordic resource of knowledge within operator algebra.