Ergodic Theory of Groups

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Ergodic Theory of Groups

Semester
SoSe 2020

Lecturer
Clara Löh

Type of course (Veranstaltungsart)
Vorlesung

Contents
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:

ubiquity of normal real numbers
existence of arbitrarily long arithmetic sequences in sets of integers of positive density
the computation of rank gradients of groups
the computation of Betti number gradients of groups
rigidity of lattices in Lie groups
approximation properties of simplicial volume
...

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.

Recommended previous knowledge
All participants should have a firm background in Analysis I/II (in particular, basic point set topology), in Linear Algebra I/II, in basic group theory (as covered in the lectures on Algebra), and in probability theory (as covered in the standard Wahrscheinlichkeitstheorie course). Knowledge on algebraic topology or group cohomology is not necessary, but might allow us to treat more interesting applications.

Time/Date
Tue 10--12, Wed 8:30--10

Location
Tue M 102, Wed M 103

Course homepage
http://www.mathematik.uni-regensburg.de/loeh/teaching/erg_ss2020/
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for the exercise classes: via GRIPS, during the first week
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of the credits, presentation of
a solution in class

Examination (Prüfungsleistungen)

Oral exam: Duration: 25 minutes, Date: individual, re-exam: Date: individual

Regelungen bei Studienbeginn vor WS 2015 / 16

Benotet:
- O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
Unbenotet:
- O. g. Studienleistung

Modules
BV, MV, MGAGeo

ECTS
9

Druckansicht