turkmath.org

Under appropriate encoding and identification, the study of the relative complexity of various classification problems can be seen as the study of the corresponding definable equivalence relations on Polish spaces. In this talk, we will introduce the framework provided by descriptive set theory to study such classification problems and analyze the complexity of the isomorphism relation of certain topological dynamical systems. We will also discuss the connections with group theory and try to understand the complexity of classification problem for infinite finitely generated simple amenable groups.