Dan Ursu, Department of Pure Mathematics, University of Waterloo
"Tracial and ideal structure of crossed products and related constructions"
This thesis concerns itself with group C*-algebras, crossed products, and groupoid C*-algebras. We are in particular interested in studying two basic pieces of structure on such algebras. The first is describing the tracial structure in a nice way (for C* and von Neumann crossed products), fixing some results of Bédos and Thomsen in the case of abelian groups along the way. The second is answering questions about the ideal structure of such algebras, and in particular obtaining extra characterizations of when they are simple or satisfy some form of relative simplicity. This generalizes much of the work done by Breuillard, Haagerup, Kalantar, Kawabe, Kennedy, and Ozawa throughout several papers.