## Admission Requirements

An introductory course to measure theory is advised. If you would like to take the course, but have no knowledge of measure theory, then please contact one of the lecturers.

## Description

Ergodic theory is a branch of mathematics that studies dynamical systems from a measure theoretic point of view. 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 typical behaviour of a dynamical system when it is allowed to run for a long time. Complementary to this typical behaviour is the exceptional behaviour, which usually happens on fractal subsets of the state space. This course focuses on the interplay between these two aspects.

## Course Objectives

The goal of this course is to introduce students to relatively new mathematical research results that merge concepts from ergodic theory and fractal geometry. These results can usually only be known by studying research papers and monographs. Students will study and present (both by writing a small paper/lecture notes, and orally) a for them new part of mathematics.

## Mode of instruction

Introductory lectures 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 and give the lecture.

## Assessment method

The grade will be determined by active participation (10%) two small oral presentations on homework exercises (20% each) and the 45 minute presentation and accompanying lecture notes (50%).

## Literature

Handouts and research papers will be provided during the course and there will be a list of references to freely accessible lecture notes.

## Contact

For more information please email Charlene Kalle or Evgeny Verbitskiy.