Geometric Analysis at the Freie Universität Berlin

Lectures and Seminars for Graduate and Undergraduate Students
Winter 2017-2018


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 - Differentialgleichungen II - BMS (Ecker)

This course will mainly deal with linear partial differential equations (PDE), and will build in particular on the material of the course on Differential Equations I as taught in the summer terms of 2011, 2013, 2015 and 2017. The content is a selection of the following:

Prerequisites : Differential Equations I

Wird in der Vorlesung bekannt gegeben.

Di 10:00 - 14:00 Uhr, SR 210/A3 Seminarraum (Arnimallee 3-5)

Do 10:00 - 12:00 Uhr, SR 009/A6 Seminarraum (Arnimallee 6)
Die erste Übung findet am 23. November statt.
Blatt 1, Abgabe am 21.11.2017 pdf | english
Blatt 2, Abgabe am 28.11.2017 pdf | english
Blatt 3, Abgabe am 5.12.2017 pdf | english
Blatt 4, Abgabe am 12.12.2017 pdf | english
Blatt 5, Abgabe am 19.12.2017 pdf
Blatt 6, Abgabe am 16.01.2018 pdf
Blatt 7, Abgabe am 23.01.2018 pdf
Blatt 8, Abgabe am 30.01.2018 pdf
Blatt 9, Abgabe am 6.02.2018 pdf

Klausur: 13.02.18 im SR 210/A3 von 10 - 12 Uhr
Noten auf dieser Webseite am 14.2.18 ab 16 Uhr
Klausureinsicht: 15.02.18 im Raum 133/A3 HH von 12 - 13 Uhr
Nachklausur: 16.04.18 im SR 140/A7 von 12-14 Uhr

Exam: 13.02.18 in SR SR 210/A3, 10 - 12 a.m.
Your grades will be posted (listed by enrolment numbers) on our website from 4 p.m. on Wednesday 14/2/18
You will have the opportunity to look at your graded exam papers on 15.02.18 from 12 noon until 1 p.m. in room 133/A3 (rear building)
Make up exam: 16.04.18 in SR 140/A7 from noon until 2 p.m.


V - Differentialgeometrie III - BMS (Afuni)

This course shall be a continuation of Differential Geometry II as taught last semester. The goal shall be to work towards a better understanding of the differential geometric and analytic tools underpinning geometric variational problems arising from modern physical theories and differential geometric considerations, with a focus on gauge theory and spin geometry in particular. Depending on the audience and demand, we shall also consider geometric evolution equations that naturally arise in these settings.

Its content shall be a selection of the following topics:

Prerequisites: Differential geometry II

R. L. Bishop and S. I. Goldberg. Tensor Analysis on Manifolds. Dover Publications, 1980.
I. Kolář, P. W. Michor and J. Slovák. Natural Operations in Differential Geometry. Springer-Verlag, 1993.
F. Warner. Foundations of Differentiable Manifolds and Lie Groups. Scott, Foresman and Company, 1971.
W. Poor. Differential Geometric Structures. Dover Publications, 1981.
D. Bleecker. Gauge Theory and Variational Principles. Dover Publications, 1981.
C. Chevalley. The Algebraic Theory of Spinors. Columbia University Press, 1954.
W. Greub, S. Halperin and R. Vanstone. Connections, Curvature, and Cohomology Vol. I. Academic Press, 1972.
W. Greub, S. Halperin and R. Vanstone. Connections, Curvature, and Cohomology Vol. II. Academic Press, 1973.
J. Roe. Elliptic operators, topology and asymptotic methods. Chapman & Hall/CRC, 1999.

Further references will be announced during the course.

Mi 10:00 - 12:00 Uhr, SR 031/A7 (Arnimallee 7)


Mi 12:00 - 14:00 Uhr, Hs 001/A3 Hörsaal (Arnimallee 3-5)

Blatt 1, Abgabe am 08.11.2017 pdf
Blatt 2, Abgabe am 15.11.2017 pdf
Blatt 3, Abgabe am 22.11.2017 pdf
Blatt 4, Abgabe am 29.11.2017 pdf
Blatt 5, Abgabe am 13.12.2017 pdf
Blatt 6, Abgabe am 20.12.2017 pdf
Blatt 7, Abgabe am 17.01.2018 pdf
Blatt 8, Abgabe am 24.01.2018 pdf
Blatt 9, Abgabe am 31.01.2018 pdf
Bonusaufgaben, Abgabe am 14.02.2018 pdf


S - Forschungsseminar Geometrische Analysis (Ecker)

Inhalt: Forschungsseminar Geometrische Analysis
Mo 16:00 - 18:00, SR 130/A3 Seminarraum (Hinterhaus) (Arnimallee 3-5)

S - Seminar Geometrische Analysis (Ecker)

Interessenten für dieses Seminar möchten sich bitte direkt per Email bei Frau Björner melden.

Der erste Seminarvortrag findet nach ca. vier Wochen statt. Die Anzahl der Seminarteilnehmer ist auf 10 begrenzt, um den Vortragenden genügend Zeit zur Vorbereitung zu geben.

Richtet sich vorrangig an Hörer nach dem Grundstudium mit Interesse an Differentialgleichungen und/oder Differentialgeometrie.

Mo 14:00- 16:00 Uhr, SR 130/A3 Seminarraum (Hinterhaus) (Arnimallee 3-5)

Sprechstunde Prof. Ecker

Die Sprechstunde von Herrn Ecker fällt wegen Krankheit bis auf weiteres aus.


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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