Ergodic Theory of Groups, SS 2020

Prof. Dr. C. Löh / J. Witzig

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Ergodic Theory of Groups

Ergodic theory is the theory of dynamical systems, i.e., of measure preserving actions of groups on probability spaces. Such systems often occur in models of real-world phenomena. But also in theoretical mathematics, dynamical systems have a wide range of applications, e.g., in the following contexts: In this course, we will introduce the basics of ergodic theory. We will then focus on group-theoretic properties and applications. Depending on the background and the interests of the audience, we might also discuss applications in geometric topology.

For additional excitement, we will aim at implementing a suitable fragment of the theory in a proof assistant (and thereby providing computer-verified proofs). Such tools are also used in the formalisation and verification of software systems.

If all participants agree, this course can be held in German; solutions to the exercises can be handed in in German or English.

Time/Location

Tuesday, 10:15--12:00, M 102,
Wednesday, 8:30--10:00, M 103.

In view of the COVID-19 pandemic, until further notice, this course will be taught remotely, based on: More details: pdf.

Exercise class

Possibly: Friday, 10:15--12:00, M 104

Read me! Lecture notes, schedules and assignments

The lecture notes will grow during the semester and will be continuously updated. The first upload is scheduled for April 21, after the first lecture. In subsequent weeks with remote teaching, I will always try to provide the material for the whole week n + 1 on the Wednesday of week n. Topics covered so far: This course will not follow a single book. Therefore, you should individually compose your own favourite selection of books. A list of suitable books can be found in the lecture notes.

Weekly assignments:

Try me! Quick checks and interactive tools

Interactive tools:

Hack me! Implementation

We will implement a fragment of the theory in the proof assistant Isabelle.

Ask me! Interactive sessions

There will be a forum and other communication tools linked on the GRIPS page of this course.

Solve me! Exercise sheets

Solutions can be submitted in English or German and in teams of up to two people. Please do not forget to add your name to all your submissions!

Is it for me? Prerequisites



Last change: July 1, 2020.