Konstantin Fedorovskiy

The concept of a Nevanlinna domain is the special analytic characteristic of bounded simply connected domains in the complex plane. It plays a crucial role in recent advances in problems of uniform approximation of functions on compact sets in the plane by polynomial solutions of elliptic equations with constant complex coefficients. The properties of Nevanlinna domains deeply relate with the properties of bounded univalent functions belonging to model spaces (that is to subspaces of the Hardy space $H^2$, which are invariant with respect to the backward shift operator). One of the most interesting problem concerning Nevanlinna domains is the following question which was posed in the early 2000s: how large (in the sense of dimension theory) there can be boundaries of Nevanlinna domains? In the talk it is planned to explain the history of this question and present it’s final solution which was recently obtained by Yurii Belov, Alexander Borichev and the author.