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401-3376-18L 8 Credits DR , MSC D-MATH

Homogeneous Dynamics and Arithmeticity

Lecturers & Examiners: Prof. Dr. Manfred Einsiedler
VVZ CR n/a

Last Updated: 2026-06-03 00:14:18

Abstract

We continue our development of homogeneous dynamics by discussing Ratner's measure classification theorems and corollaries thereof. We will also discuss various applications of the general theory. However, a big portion of the course will focus on the Margulis strategy for proving arithmeticity of lattices and the more recent result by Bader-Fisher-Miller-Stover.

Objective

Theory, Proofs, and Connections of the topic to other areas: - Special cases of Ratner's measure classification theorems - Linearisation technique, which gives orbit and equidistribution theorems as corollaries of the measure classification - Arithmeticity of Lattices in higher rank setting - Arithmeticity for hyperbolic manifolds - Applications to Diophantine approximation and other topics

Content

The course will give detailed proofs. The most prominent exception will be Ratner's measure classification, where we will only treat special cases.

Resources

Lecture Notes

We will follow the same book project, which in the course of the semester will contain more and more of the topics of the course:https://tbward0.wixsite.com/books/homogeneous

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
oral 30 minutes
The exam is only offered in the Examination Sessions Summer 2026 and Winter 2027.30 minutes preparation and 30 minutes exam (one candidate prepares during the 30 minutes oral exam of the previous candidate).[Open-Book während der 30 Minuten Vorbereitung und dann 30 Minuten Prüfung ohne Buch.]

Course Components

Type Title Time & Place Hours
lecture Homogeneous Dynamics and Arithmeticity ( = Homogeneous Dynamics and Applications, Part II)
  • Mon 14:15-16:00 (HG D 7.2)
  • Fri 12:15-14:00 (HG D 1.1)
4 h weekly

Offered In