Research

The subject of my  research is mainly operator algebras – in specific, classification of C*-algebras and the interplay between C*-algebras and symbolic dynamics.

In the past decades, the subject of operator algebras, which serves as a mathematical foundation of quantum mechanics, has seen an enormous expansion and has attracted many eminent mathematicians, including the Fields medallists Connes and Jones. The application of techniques and results from operator algebra to dynamical systems has in particular developed rapidly in recent years. Already John von Neumann was interested in the interaction between operator algebra and dynamics. The interface between these two mathematical theories establishes a connection between two well established, but quite different mathematical areas, and has turned out to be well worth studying, both from the point of view of operator algebra and from the point of view of dynamics. 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 intensive exchange of ideas. Among the concrete results are new invariants for dynamical systems and series of new examples of C*-algebras.