Universität Wien

250118 SE Geometric Analysis (2023W)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
ON-SITE
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 07.12. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.12. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.12. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.01. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.01. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.01. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.01. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.01. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.01. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The goal of this seminar is to build up working knowledge for research in geometric analysis. For a large part of the seminar, we will follow the book »Geometric Analysis« by Peter Li, which is available online through the university catalogue. In particular, we will cover the following topics from Li's book.

- Bochner-Weitzenböck formulas
- Poincare inequality and the first eigenvalue
- Gradient estimate and Harnack inequality
- Mean value inequality
- Reilly's formula and applications
- Isoperimetric inequalities and Sobolev inequalities
- Linear growth harmonic functions
- Polynomial growth harmonic functions
- L^q harmonic functions

Students will give presentations on these topics and answer related questions of their peers and the seminar conveners. Occasionally, students will be asked to submit written solutions to problems provided by the conveners.

Prerequisite for participation in this course is a working knowledge of Riemannian Geometry on the level of 250070 VO Riemannian Geometry (2023W).

Assessment and permitted materials

- 2-3 45-minute-presentations on the course material
- answering questions on their presentations by their peers and the course conveners
- cross-reading of each chapter before its presentation; preparation of thought-out questions

Minimum requirements and assessment criteria

Examination topics

Reading list

Li, P. (2012). Geometric Analysis (Cambridge Studies in Advanced Mathematics). Cambridge: Cambridge University Press.
doi:10.1017/CBO9781139105798

Association in the course directory

MGES; MANS

Last modified: We 15.11.2023 09:09