Universität Wien
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250097 VO Homogeneous Dynamics (2022S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 01.03. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.03. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.03. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.03. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.03. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.04. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.04. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.05. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.05. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.05. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.05. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.05. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.06. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.06. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.06. 09:45 - 11:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The course consists in an introduction to the study of homogeneous flows, which are smooth flows on (quotients of) Lie groups obtained by multiplication by a 1-parameter subgroup. In particular, we will focus on the ergodic theory of Heisenberg nilflows and of geodesic and horocycle flows. We will also explore some connections with problems in number theory.
No prior knowledge in Lie group theory is assumed and all the relevant objects will be introduced during the lectures. However, some familiarity with basic notions in ergodic theory is recommended.
Lecture notes will be made available during the course.

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

Understanding and working knowledge of the material discussed in the lectures.

Examination topics

All the material covered in the lectures is subject of examination. The student should also be able to solve simple exercises, which will be assigned during the lectures.

Reading list

Lectures notes will be made available to the participants.
Additional useful material is:
- M. Einsiedler, T. Ward. Ergodic Theory with a view towards Number Theory. Graduate Texts in Mathematics 259, Springer, London, 2011.
- J.M. Lee Introduction to Smooth Manifolds. Graduate Texts in Mathematics 218, Springer, New York, NY, 2012.
- M.B. Bekka, M. Mayer. Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces. London Mathematical Society Lecture Note Series 269, Cambridge University Press, Cambridge, 2000.

Association in the course directory

MSTV

Last modified: Th 26.10.2023 00:23