Getz, Alan

Project title: Applications of the Continuous Model Theory of C*-Algebras to Cantor Dynamical Systems

Department: Mathematics and Statistics

Faculty supervisor: Dr. Christopher Eagle

"The study of topological dynamics of Cantor spaces is a vibrant branch of pure mathematics with connections to the study of AF algebras and K-theory via the examination of Bratteli diagrams.  Moreover, the field has seen numerous applications in areas such as computer science and electrical engineering.  Gelfand duality provides a link between these dynamical systems and C*-algebra theory, and so the aim of this project would be to apply recent developments in the continuous model theory of the latter to the study of the former.  In particular, I hope to characterize the generic homeomorphism of the Cantor set purely in terms of the model theory of its corresponding C*-algebra."