Minicourse “Geometry of the unit ball in various holomorphic spaces”

St. Petersburg State University and Euler International Mathematical Institute are happy to announce a new minicourse, headed by prof. Konstantin Dyakonov (ICREA and Universitat de Barcelona). Lectures (60 minutes each) are scheduled on Thursday, November 25, Tuesday, November 30 and Thursday, December 2, starting at 5pm. To attend the lectures, please join zoom channel (511-327-649). Video records of the course are available here.

Course description

When studying the geometry of a certain Banach space $X$ , one often needs to determine the extreme points of its closed unit ball, $b(X)$ . Among these, an interesting subset is formed by the so-called exposed points. (By definition, a point of $b(X)$ is exposed for the ball if there is a hyperplane in $X$ that touches $b(X)$ at that point only.) In this minicourse, our purpose is to characterize the extreme — and sometimes exposed — points of the unit ball in several holomorphic spaces. In particular, this will be done for subspaces of the Hardy spaces $H^1$ and $H^\infty$ that consist of functions with prescribed spectral gaps. Also, we shall take a look at model subspaces and Toeplitz kernels in these Hardy spaces.

Everyone is welcome!

Lecture 1. Slides

Lecture 2. Slides

Lecture 3. Slides