Aspects of automatic continuity.

I will present an overview and some more specialised topics related to automatic continuity in the context of Polish groups. Apart from its intrinsic interest, the topic of automatic continuity touches on many different aspects of topological groups and has led to numerous interesting concepts and discoveries. In particular, I will discuss the many facets of the closed graph theorem, its application to a problem of JPR Christensen and a set theoretical quadrichotomy regarding the behaviour of homomorphisms between Polish groups. Time permitting, I will also discuss topological rigidity of automorphism groups of highly homogeneous separable complete metric first-order structures.