Geometric Analysis at the Freie Universität Berlin

Summer 2019

Lectures

**V -Partielle Differentialgleichungen I (Ecker) **

**Course Content**

A selection of topics from the following:

- Examples of partial differential equations
- Euler Lagrange equations
- Transport equation
- Laplace - and Poisson equation
- Heat equation
- Maximum principles
- A priori estimates
- Wave equation
- Energy methods
- Representation formulas
- Solution methods
- Introduction to Hilbert space methods

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

**Literature:
**L.C. Evans, Partial Differential Equations

W.A. Strauss, Partial Differential Equations, an introduction

These books are available in the library.

**Prerequisites:** PDF

**Lecture:**

Tuesday 14:00 - 18:00, A6/SR 007/008

**Tutorials:**

Monday 12:00 - 14:00,
A3/SR 119

Monday 14:00 - 16:00,
A3/SR 019

The tutorials on Monday 29.4 will be used for revision of prerequisites from Analysis 2 and 3. For the topics refer to the prerequisites.

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

Participation in the tutorials in compulsary (Anwesenheitspflicht in den Übungsgruppen).

**Problem sheets:**

Sheet 1, due 30/04/2019 at 2 PM pdf

Sheet 2, due 07/05/2019 at 2 PM pdf

Sheet 3, due 14/05/2019 at 2 PM pdf

Sheet 4, due 21/05/2019 at 2 PM pdf

Sheet 5, due 04/06/2019 at 2 PM pdf

Sheet 6, due 11/06/2019 at 2 PM pdf

Sheet 7, due 18/06/2019 at 2 PM pdf

Sheet 8, due 25/06/2019 at 2 PM pdf

To give you enough time to revise the lecture material before solving problems, the first problem sheet will be handed out to you on Tuesday 23 April 2019, that is in week 3 of semester. This is due back on Tuesday 30 April 2019.

Since the 22.4.2019 is Easter Monday, the first tutorials will be on Monday 29 April 2019.

As you will not have handed in your solutions on that date I will take the opportunity to revise relevant material from Analysis 2 and 3 and from the PDE lectures. Because of the public holiday of Pentecost (Pfingsten) there will also be no tutorials on Monday 10 June 2019.

Please hand in your worked solutions in groups of three.

**Written exam:**

Tuesday 9 July, 2019 (2 - 4 pm in room A6/SR 007/008)**
Klausurergebnisse: PDF
Opportunity to look at your exam results**: 16 July, 2019, 2 - 3 pm in room 133 (Arnimallee 3)

**Make-up exam:** Monday 7 October, 2019, 12 - 2 pm in SR 032 (Arnimallee 6)

**Make-up exam results:** HTML

**Opportunity to look at your make-upexam results**: Thursday October 31, 12-1 in room 132 (Arnimallee 3, rear building)

**V - Differentialgeometrie II (Ahmad Afuni) **

**Course Content**

This course shall deal with Riemannian geometry in the large. It shall be a continuation of Differential Geometry I and also serve as preparation for modern developments in geometric analysis and mathematical physics. Its content shall be a selection of the following topics:

- basic notions of differential topology
- geodesics, the exponential mapping and the Hopf-Rinow theorem
- comparison theorems and connections between curvature and topology
- differential forms, Stokes' theorem and de Rham cohomology
- spaces of constant curvature, Lie groups and homogeneous spaces
- isometries, Killing fields and the Myers-Steenrod theorem

Literature: to be announced.

**Lecture:**

Tuesday 10:00 - 14:00, A6/SR 007/008

**Notes:**

pdf

**Tutorial:**

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

**Tutorial sheets:**

Sheet 1, due 03/05/2019 pdf

Sheet 2, due 10/05/2019 pdf

Sheet 3, due 17/05/2019 pdf

Sheet 4, due 24/05/2019 pdf

Sheet 5, due 31/05/2019 pdf

Sheet 6, due 07/06/2019 pdf

Sheet 7, due 14/06/2019 pdf

Sheet 8, due 21/06/2019 pdf

Sheet 9, due 02/07/2019 pdf

**Written exam:**

Wednesday 10 July, 2019 at 10 AM sharp, SR 031/A7 (Arnimallee 7)

Formula sheet

Seminars

**S - Forschungsseminar Geometrische Analysis (Ecker) **

Forschungsseminar Geometrische Analysis

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

This seminar is recommended for MSc and PhD.

**S - Seminar Partielle Differentialgleichungen (Ecker) **

**Inhalt: **

This seminar can be taken concurrently with the lecture course on Introduction to Partial Differential Equations.

It may serve as the basis for a BSc and/or MSc project.

**Updated information sheet including final list of talks**:

PDF

**Location and venue:**

Monday 10:00- 12:00,
SR 130/A3 Seminarraum (Arnimallee 3 HH)

There will be a **second short organizational meeting** on Monday 06.05.2019 at 11.30 am (sharp) in room 130/A3HH. Attendance at this meeting is compulsory. Please carefully read the updated information sheet beforehand.

The first talk will be on Monday 20.05.2019. I have been able to accommodate all your requests regarding the topics.

Sprechstunde Prof. Ecker

Dienstag von 13:00 - 14:00 Uhr.Wegen großer Nachfrage nur mit Voranmeldung: bjoerner@math.fu-berlin.de.

Archiv

Wintersemester 2018/2019

Sommersemester 2018

Wintersemester 2017/2018

Sommersemester 2017

Wintersemester 2016/2017

Sommersemester 2016

Wintersemester 2015/2016

Sommersemester 2015**
Wintersemester 2014/2015
Sommersemester 2014
Wintersemester 2013/2014
Sommersemester 2013
**Wintersemester 2012/2013

Sommersemester 2012

Wintersemester 2011/2012

Sommersemester 2011

Wintersemester 2010/2011

Sommersemester 2010

Wintersemester 2009/2010

Sommersemester 2009

Wintersemester 2008/2009

Sommersemester 2008

Wintersemester 2007/2008

Sommersemester 2007

Wintersemester 2006/2007

Sommersemester 2006

Wintersemester 2005-2006

Sommersemester 2005

Wintersemester 2004-2005

Sommersemester 2004