Operator Structures and Dynamical Systems

21 - 25 July 2008

Venue: Lorentz Center@Oort

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This workshop is an official satellite of the fifth European Congress of Mathematics in Amsterdam in the preceding week.  Many dynamical systems are accompanied by an operator structure which encodes essential traits of the dynamics. The principal aim of this workshop is to enhance the exchange of knowledge and ideas between researchers from various countries, research groups and levels of seniority, who are all interested in the relation between dynamical systems and the attached operator structures, as well as to facilitate establishing new collaborations between these researchers. A well known instance of the above situation is that of a topological group acting on a compact Hausdorff space via homeomorphisms. One can then form the associated crossed product C*-algebra, which is the counterpart of the crossed product von Neumann algebra associated with a group of measurable transformations. As is well known, the associated von Neumann algebra carries relevant information about the measurable system, and likewise the associated C*-algebra carries information about the topological system. Many results have been brought to light which relate the structure of the crossed product and the dynamical properties of the topological system. This interplay between topological dynamical systems and C*-algebras has been a stimulus for the development of the theory of crossed products of C*-algebras in the early days and is still an area of active research. The above is a special case of a more general setting where a group acts on a possibly noncommutative C*-algebra rather than on the continuous functions on a compact space, in which case it is also possible to construct a crossed product C*-algebra. The general theory of such algebras is well established and has significant bearing on the interplay between topological dynamical systems and the associated crossed product C*-algebras. Yet is not always possible to obtain the more detailed results which can sometimes be given in the commutative setting, simply by specialising the general theory, or to provide the most efficient and general proofs in that context. Hence here the general and special viewpoint supplement one another. Apart from these C*-algebras associated with invertible dynamics (be it abstract or topological) several other classes of operator structures are under current research: analytic crossed products, C*-algebras associated with non-invertible dynamics and transfer operators, Banach algebra crossed products corresponding to a Banach algebra dynamical system, etc. In this workshop researchers in all these areas are expected to be present, both from the general theory of such algebras and from the interplay with topological dynamics when this is applicable. We welcome further contributions in this vein, relating operator structures and dynamical systems, as well as applications in other disciplines.

    Marcel de Jeu  

    Klaas Landsman  

    Sergei Silvestrov  

    Christian Skau  

    Jun Tomiyama  

    Sjoerd Verduyn Lunel  

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