Teaching WS 2020/21

Lecture + seminar (4 SWS) "Operators on infinite graphs", starting Oct 27th on Tue 15:15-16:45 and Wed 11:15-12:45, SG 3-12 (in classroom phases)

Graph structures play an enormous role in science and technology, including (mathematical physics).
They also give rise to many beautiful mathematical phenomena - some of which become especially interesting
when dealing with infinite graphs. The goal of this course is to introduce infinite graphs as analytic objects
and to study the (in many cases unbounded) Laplace and Schrödinger operators arising from them.
A special focus will be on the interplay between geometric and analytic properties of the graph and spectral
theoretic features of the associated operator. A slightly more detailed course describtion can be found here.

The course is designed as a combination of a lecture and a seminar. There will be two lectures per week until the Christmas
break. Afterwards the course resumes in seminar mode and the participants present talks on subject-related topics.
There will also be the option to work together in pairs. The seminar topics will be handed out after four weeks of classes.

The target group for this course are diploma and master students having a sound knowledge of functional analysis, in particular
in the theory of unbounded linear operators on Hilbert spaces. Supplementary reading material will be provided.
The teaching language in this course is English.

This course can be taken as an online course. Within the framework given by the current regulations we will arrange for as much
classroom teaching as possible, in particular during the seminar phase. Please enroll in the moodle2 course
(that will be set up soon). Further information will be given there in due time.

Recommended literature:

Keller, Matthias and Lenz, Daniel and Wojciechowsky, Radoslaw: Graphs and discrete Dirichlet spaces,
book in preparation, 2020+

Nagel, Rainer: A short course on operator semi-groups,
Springer Berlin Heidenlberg New York.

Reed, Michael and Simon, Barry: Methods of Modern Mathematical Physics I: Functional Analysis.
Academic Press New York and London.

Reed, Michael and Simon, Barry: Methods of Modern Mathematical Physics II: Fourier analysis, self-adjointness.
Academic Press New York and London.

Reed, Michael and Simon, Barry: Methods of Modern Mathematical Physics IV: Analysis of operators.
Academic Press New York and London.

Schmüdgen, Konrad: Spectral theory of Unbounded Self-adjoint operators of Hilbert space.
Graduate Text in Mathematics, Springer Heidelberg New York London.

Weidmann, Joachim: Lineare Operatoren in Hilberträumen I: Grundlagen. (for German speakers)
Teubner Stuttgart Leipzig Wiesbaden.

Werner, Dirk: Funktionalanalysis. (for German speakers)
Springer Spektrum Berlin.

Vorlesung (4 SWS) "Ergodentheorie", ab 26.10. jeweils Mo 11:15-12:45 und Di 9:15-10:45, A-314 (in Präsenzphasen)

Die Vorlesung gibt eine Einführung in die Welt topologischer und maßtheoretischer Systeme.
Wir beweisen zentrale Konvergenzsätze und studieren einige spannende Anwendungen aus der
Zahlentheorie. Eine detaillierte Ankündigung ist hier zu finden.

Vorausgesetzt werden Verständnis des Stoffes des Grundstudiums, sowie Basiskenntnisse in Funktionalanalysis.

Die Vorlesung kann als Online-Kurs belegt werden. Darüber hinaus sollen innerhalb der dann aktuell geltenden
Regelungen so viele Präsenzphasen wie möglich stattfinden. Bitte schreiben Sie sich in den
moodle2-Kurs ein, der bald eingerichtet wird. Weitere Informationen werden dort zu gegebener Zeit gegeben.

This course can also be given in English. In case of any questions, just send an email.


Manfred Einsiedler and Tom Ward: Ergodic Theory with a view towards Number Theory,
Graduate Texts in Mathematics 259, Springer, 2011

Tanja Eisner, Balint Farkas, Markus Haase and Rainer Nagel: Operator Theoretic Aspects of Ergodic Theory,
Graduate Texts in Mathematics 272, Springer, 2015

Hillel Furstenberg: Recurrence in ergodic theory and combinatorial number theory,
Princeton University Press, Princeton NJ, 1981

Peter Walters: An Introduction to Ergodic Theory ,
Graduate Texts in Mathematics, Springer, 1982