Geometric Analysis at the Freie Universität Berlin

Lectures and Seminars for Graduate and Undergraduate Students
Summer 2018


The International Max-Planck Research School for Geometric Analysis, Gravitation and String Theory is a joint project of the Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Freie Universität Berlin (Institute for Mathematics) and Universität Potsdam.
The IMPRS aims to promote research in mathematical physics in an area related in the widest sense to Einstein's theory of general relativity, ranging from pure mathematics (differential geometry and the theory of partial differential equations) to the physics of black holes, gravitational waves and cosmological applications of Einstein's theory and all the way to the most recent efforts to reconcile Einstein's theory with quantum mechanics in the framework of superstring theory and M theory.

Our following seminars are recommended for post-graduates of the IMPRS:
- - Forschungsseminar Geometrische Analysis.
- - Topics in Geometric Analysis (AEI - FU - UP)



V - Partielle Differentialgleichungen III - (Ecker)

The content is a selection of topics from the following areas:

Wird in der Vorlesung bekannt gegeben.

Di 10:00 - 12:00 Uhr, SR 130/A3 (Arnimallee 3 HH)

Di 12:00 - 14:00 Uhr, Raum 1.1.53/A14 (Arnimallee 14)


V - Spezialvorlesung Topics in Geometric Evolutions Equations (Ecker)

Geometric evolution equations like the Ricci flow and the mean curvature flow have played an important role in the solution of several major open conjectures in geometry and topology like for instance the Poincare conjecture and Thurston's geometrization programme. We shall present some selected techniques related especially to the work of Perelman on Ricci flow on closed manifolds and discuss adaptations of this when boundary terms are involved. This will in particular include the lecturer's own research carried out over the last few years, part of which has been published and some of which is still work in progress. Although this lecture course is aimed at students at the MSc and PhD level (postdocs are also welcome) it does not require a lot of background material except for the one listed below.
Note that this lecture course is NOT a replacement for Partielle Differentialgleichungen 3!

Diff. Geom. 1, Partielle Differentialgleichungen 1, Familiarity with Riemannian manifolds, hypersurfaces, curvature, Sobolev spaces and inequalties and some basic regularity thory for PDE will definitely be assumed. More advanced background material will be presented in lectures.

To be advised in class

Do 10:00 - 12:00 Uhr, Raum 119/A3 (Arnimallee 3)

V - Introduction to General Relativity (Afuni)

The theory of general relativity is one of the crowning achievements of modern mathematical physics having not only pushed the boundaries of the field of differential geometry, but also having found applicability in the real world, particularly in GPS technology. This course shall deal with the mathematical foundations and formulation of general relativity as well as the recently proved positive mass theorem. It shall begin with the geometry of Minkowski spacetime, which forms the basis of Einstein's special theory of relativity and adequately describes the geometry of general relativity in the small, followed by an account of Lorentzian geometry and its tensor calculus. We shall then introduce Einstein's equation and discuss exact solutions. We shall then turn our attention to modern developments, culminating in a proof of the positive mass theorem. We shall also discuss field theories unifying gravity and other forces of nature; though these have been unsuccessful from the physical point of view, they give rise to interesting geometries.


Mi 12:00 - 14:00 Uhr, Raum 210/A3 (Arnimallee 3)


S - Forschungsseminar Geometrische Analysis (Ecker)

Forschungsseminar Geometrische Analysis

Mo 16:00 - 18:00, SR 130/A3 (Arnimallee 3 HH)


S - Seminar/Forschungsmodul Partielle Differentialgleichungen (Ecker)

Diese Veranstaltung richtet sich an studierende auf dem Gebiet der partiellen Differentialgleichungen.  Es wird vorausgesetzt, dass diese die Vorlesungen Partiellen Differentialgleichungen 1 und 2 gehört haben.

Es werden über die Vorlesung hinausgehende Themen aus diesem Gebiet behandelt.

Mo 14:00- 16:00 Uhr, SR 130/A3 Seminarraum (Arnimallee 3 HH)

Interessenten bitte per email beim Dozenten melden.

S - Seminar/Forschungsmodul Differentialgeometrie (Afuni)

Dieses Seminar setzt die Kurse 'Differentialgeometrie II' und 'Differentialgeometrie III' fort und ergänzt das dort Gelernte. Außerdem schließt es das Modul 'Differentialgeometrie III' ab. Sein Inhalt besteht aus fortgeschrittenen Themen aus der Differentialgeometrie mit Neigung zu Riemannscher Geometrie, Eichtheorie und Spin-Geometrie.

Mi 14:00- 16:00 Uhr, Raum 031/A7 (Arnimallee 7)

Sprechstunde Prof. Ecker
Montags 15:00 - 16:00 Uhr.
Wegen großer Nachfrage nur mit Voranmeldung:


Bürozeiten Ann Björner
Montag 11:00 - 15:00 Uhr 
Dienstag 12:00 - 16:00 Uhr 
Mittwoch 11:00 - 15:00 Uhr 
Donnerstag 10:30 - 14:30 Uhr 
Freitag geschlossen



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