Title: New solution of a problem of Kolmogorov on width asymptotics in holomorphic function spaces.

Abstract: In this talk we will discuss the notion of epsilon-entropy and the related notion of n-widths introduced by Kolmogorov in the 1950s, as a measure of the complexity of compact sets in a metric space. We will then discuss a new proof for a problem originally raised by Kolmogorov on the precise asymptotics of the epsilon-entropy of compact sets in spaces of holomorphic functions which relies on a reformulation in terms of Toeplitz operators on weighted Bergman spaces, exhaustion procedures by special holomorphic polyhedra and ideas from pluripotential theory.