Research on the Classification of Nuclear C*-Algebras

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AbstractDadarlatThe investigator aims at developing techniques of K-theory and local approximation suitable for the classification theory of nuclear C*-algebras. In particular, the investigator will explore new models for the KK-groups of Kasparov. On the analytical side he would focus on local approximation properties such as quasidiagonality and its refinements.The basic idea beyond the classification program is that that the simplicity and other nonstable K-theory conditions for a nuclear C*-algebra translate to certain internal dynamical properties of the algebra. In their turn, these properties lead to surprising rigidity phenomena where an algebra is completely determined by its homotopy type or even by its K-theory groups.C*-algebras can be thought as collections of infinite matrices of numbers displaying a rich algebraic and topological structure. The C*-algebra theory is the standard framework for quantum mechanics. It offers functional analytic ways of expressing and analysing fundamental noncommutative aspects of the symmetries of the physical world. The proposed research will attempt to uncover and explain rigidity properties of nuclear C*-algebras. This theory has deep ramifications in dynamical systems and geometric theory of groups.