Classification of C*-dynamics: noncommutative symmetry and time evolution

Within the last few years, our understanding of simple amenable C*-algebras has advanced enormously. These objects arise as noncommutative topological spaces that are in a sense indecomposable, and new insights about them have traditionally led to input into other mathematical areas and even physics. The recent highlight is a satisfactory classification theory for simple amenable C*-algebras utilizing computable invariants such as topological K-theory. The objective of this project is to classify dynamical systems inherent to simple amenable C*-algebras, which includes time evolutions as well as actions of discrete groups, in part by capitalizing on these new techniques. A high degree of rigidity is expected in the types of dynamics having an amenable and outer origin, which will be explored with novel methods related to equivariant Kasparov theory and noncommutative ergodic theory.