Structure and dynamics of Polish groups conference

Polish topological groups comprise all locally compact second countable groups, but also most interesting topological transformation groups such as homeomorphism and diffeomorphism groups of compact manifolds, isometry groups of separable complete metric spaces, and automorphism groups of countable model theoretical structures. While all of these classes had been intensively studied separately, there has recently been great progress on the general theory of non-locally compact Polish groups. The systematic study of those groups and their actions was initiated in descriptive set theory, where the emphasis was on the complexity of their orbit equivalence relations. More recently, however, it has grown into an independent field that has developed connections with many other areas. For example, the topological dynamics of automorphism groups is intimately related with combinatorics and structural Ramsey theory; understanding their measure-preserving actions has applications to probability theory. Much progress has been made in understanding their representations on Hilbert and other Banach spaces as well as developing geometric group theory in this more general setting. The conference will bring together specialists on automorphism groups of model-theoretic structures, general Polish groups, and dynamics.