# Operator algebra (completed)

The operator algebra group is a national network with members from the University of Oslo (UiO), Oslo University College (HiO) and the Norwegian University of Science and Technology (NTNU). The present project aims at conducting research in leading areas of operator algebras, strengthening and expanding the groups large international contacts, renewing the bonds between Trondheim and the two branches of the network in Oslo, and educating young scientists to continue the work. Several principal directions of research will be pursued during the project.

Summary of the scientific goals of the project: show for a large class of groups (conjecturally all amenable ones) that minimal actions are orbit equivalent to integer-actions; develop a theory of noncommutative geometry for quantum groups and their homogeneous spaces, including an algebraic index theorem; identify data of arithmetic significance in quantum statistical dynamical systems from number fields, and explore tantalizing links between number theory and ergodic theory; describe the structure of C*-algebras arising in the study of actions of semigroups and Hecke-pairs, shift spaces and higher-rank graphs; advance the theory of finite quantum systems by operator algebraic methods; attract new Ph.D.-students and postdocs to ensure a high level of research in operator algebras in Norway; revitalize and strengthen the scientific connection between the members at UiO, HiO and NTNU.

Project number: 191195/V30 of the Research Council of Norway.