Universität Wien

250096 SE Synthetic Geometry and Optimal Transport (2024W)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
Moodle
Mo 25.11. 09:45-11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

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

  • Monday 07.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The goal of the seminar is to explore synthetic geometry, i.e., curvature bounds for non-smooth spaces, by using the theory of optimal transport.
A rough outline of the topics to be covered is
1) Measure theory on (polish) metric spaces
2) Optimal Transport
3) Wasserstein metrics and spaces
4) Curvature bounds, CD(K,N)-spaces and compatibility to the smooth case
5) RCD-spaces
6) Applications
7) Synthetic Lorentzian geometry

Assessment and permitted materials

Preparing and giving a seminar talk, and participating in the discussions of seminar talks by fellow students.

Minimum requirements and assessment criteria

Preparing and giving a seminar talk, and participating in the discussions of seminar talks by fellow students.

Examination topics

Preparing and giving a seminar talk, and participating in the discussions of seminar talks by fellow students.

Reading list

Depending on the topic and the student's interests, current literature will be provided, but some background material is:
Cedric Villani. Optimal transport, volume 338 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 2009
Lecture notes on Optimal Transport: https://clemenssaemann.wordpress.com/wp-content/uploads/2022/07/vootclemenssaemann.pdf

Association in the course directory

MGES; MANS

Last modified: Tu 15.10.2024 00:02