Mathematical Sciences: Topological Invariants Associated to C*-Dynamical Systems

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Williams will continue his investigation of the ideal structure of crossed product C*-algebras. The primary focus will be on the interplay between topological invariants associated to a dynamical system and the structure of the resulting crossed product. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics" can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way, ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.