Pandelis Dodos: Applications of Descriptive Set Theory in the Geometry of Banach spaces

Monday June 22 to Wednesday June 24, 10:15-11:05

We will review some recent advances on the interaction between Descriptive Set Theory and the Geometry of Banach spaces. We will concentrate around problems which can be traced back to the beginnings of Banach Space Theory and asking whether certain classes of separable Banach spaces admit universal spaces with special properties. Recently, all these problems are solved and the crucial conceptual vehicle for arriving to the solution is the notion of a strongly bounded class of separable Banach spaces. Beside its intrinsic functional-analytic interest, this notion points out towards a more general phenomenon which seems to be of interest also to set theorists.