IMPRESSUM   DATENSCHUTZ
	Fakultät für Mathematik	Universität Regensburg
Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen. Note For our digital courses all relevant information can be found on the appropriate GRIPS sites. 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