Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. More recent applications include Number Theory, Fractal Geometry, and combinatorics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The goal of this course is that students get familiar with studying and presenting (both by writing a small paper/lecture notes, and orally) a for them – new part of mathematics, which usually can only be known by studying research papers or monographs. Introductory lecture will be given by Kalle and Verbitskiy, all other lectures by the participants. To do this, each participant will choose a subject from the list of subjects presented at the beginning of the course, and then will prepare lecture notes for a 45 minutes class on the chosen subject.
Handouts and research papers will be provided during the course and there will be a list of references to freely accessible lecture notes.