Universität Wien
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250030 VO Random Walks on Groups (2023S)

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

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 01.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.03. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.03. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.03. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.03. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.03. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.03. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.04. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.04. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.04. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.04. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 03.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.05. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.05. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.05. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 31.05. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 01.06. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.06. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.06. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.06. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.06. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.06. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.06. 08:00 - 09:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 29.06. 09:45 - 10:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The topic is random walks on infinite, finitely generated groups.

We will cover some classical results such as growth of the group vs transience of walks and Kesten's amenability condition. The main focus will be on connections between the geometry of the group and the behavior of random walks. The model result is the theorem of Kaimanovich that the Poisson boundary of a random walk on a hyperbolic group coincides with the Gromov boundary, so the 'random walk boundary' and the 'geometric boundary' agree. We will cover the recent construction of Qing-Rafi-Tiozzo of a sublinear Morse boundary that plays the role of the Gromov boundary in the non-hyperbolic case, with a proof that for CAT(0) groups the Poisson boundary agrees with the sublinear Morse boundary.

Prior experience with hyperbolic and CAT(0) groups is not required---these concepts will be developed in the lectures.

The Wednesday meetings will be lectures. The Thursday meetings will be discussion/exercise.

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

Pass the oral exam.

Examination topics

Contents of the course.

Reading list

Woess, Random Walks on Infinite Graphs and Groups

Yulan Qing, Kasra Rafi, Sublinearly Morse boundary I: CAT(0) spaces, Advances in Mathematics, Volume 404, Part B, 2022, https://doi.org/10.1016/j.aim.2022.108442.

Association in the course directory

MALV

Last modified: Fr 04.08.2023 15:07