Lectures and Seminars for Graduate and Undergraduate Students
Winter 2018/2019

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 - Differentialgeometrie I (Ecker)

Topics:

• Curves and n- dimensional surfaces in Euclidean space
• Metrices and Riemannian manifolds
• Notions of curvature
• Vector fields. tensor fields, covariant derivative
• Geodesic curves, exponential map

This course is a BMS course and will be held in English if requested.

References:

(Note that these are only suggestions; I will follow neither of these books exactly; they are meant to be for additional reading only)

• J. A. Thorpe, Elementary topics in differential geometry (relevant for level set and parametrized n - surfaces in Euclidean space modulo notation, sign conventions and the order in which topics are presented)
• W. Kühnel, Differential geometry, curves, surfaces, manifolds (there is also a German version)
• M. do Carmo, Riemannian geometry (note that I will adopt different sign conventions for instance for the curvature tensor; the ones I use are the international standard)
• J. Lee, Riemannian manifolds, An introduction to curvature
• Gromoll, Klingernberg, Meyer, Riemannsche Geometrie im Großen
• M. Spivak, A comprehensive introduction to differential geometry Vol I - III

Prerequisites: PDF

Vorlesung:
Dienstag 10:00 - 14:00 Uhr, SR 024/A3 (Arnimallee 3-5)

Übung:
Montag 12:00 - 14:00 Uhr, SR 140/A7 (Arnimallee 7)
Dienstag 14:00 - 16:00 Uhr, SR 1.1.53/A 14 (Arnimallee 14)
Erste Übung am 29. Oktober, bzw. 30. Oktober 2018

Übungsblätter:
Blatt 1, Abgabe am 06.11.2018 PDF
Blatt 2, Abgabe am 13.11.2018 PDF
Blatt 3, Abgabe am 20.11.2018 PDF
Blatt 4, Abgabe am 27.11.2018 PDF
Blatt 5, Abgabe am 11.12.2018 PDF
Blatt 6, Abgabe am 18.12.2018 PDF
Blatt 7, Abgabe am 14.01.2019 PDF
Blatt 8, Abgabe am 28.01.2019 PDF
Blatt 9, Abgabe am 04.02.2019 PDF
Blatt 10, lecture revision and exam preparation PDF

Please hand in your worked solutions in groups of three or four. 

Active participation in the tutorials comprises the submission of correct solutions of at least 50 percent of the weekly ecercises as well as presenting a solution at least once during the semester in one of the tutorials. 

Dieser Kurs kann auch als Basis für eine Bachelor- oder eine Masterarbeit in der Differentialgeometrie dienen.

Exam: Tuesday 12.2.1019 at 10 pm, SR 024/A3 (Arnimallee 3-5)
Klausurergebnisse
Opportunity to look at your exam results: April 1, 2019, 10 - 11 am in room 133 (Arnimallee 3)

Make-up exam: Monday 1.4.2019, 12 - 2 pm in SR 031 (Arnimallee 6)
Nachklausurergebnisse
Opportunity to look at your make-up exam results: April 8, 2019, 12 - 13 pm in room 133 (Arnimallee 3)

S - Forschungsseminar Geometrische Analysis (Ecker)

Inhalt:
Forschungsseminar Geometrische Analysis

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

 

S - Proseminar Elementare Differentialgeometrie (Ecker)

Inhalt:
Das Proseminar kann begleitend zur Vorlesung Differentialgeometrie gehört werden. Diese ist aber keine Voraussetzung hierfür.

Notwendige Voraussetzungen sind Analysis 1 und 2 und Lineare Algebra 1 und 2. Vortragsthemen werden zu Semesterbeginn bekanntgegeben. Eines der Quellen ist das Buch von Bär über Elementare Differentialgeometrie.

Dieses Proseminar ist geeignet als Vorbereitung für Bachelor-Arbeiten.

Informationsblatt PDF
Please note that talk number 9 has been cancelled and that talk number 8 will take place Monday February 4th.

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

Vorbesprechung am 15. Oktober 2018

Maximale Teilnehmerzahl: 11

 

Montag von 11:00 - 12:00 Uhr.
Wegen großer Nachfrage nur mit Voranmeldung: bjoerner@math.fu-berlin.de.

 

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