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401-5002-22L 2 Credits DR D-MATH

Dynamics on Homogeneous Spaces and New Applications to Number Theory

Lecturers & Examiners: Prof. Dmitry Kleinbock
Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to register the course unit via the Registrar's Office ( ).
VVZ CR n/a

Last Updated: 2026-02-05 16:07:27

Abstract

Nachdiplom lecture

Content

Dynamical systems on homogeneous spaces have been the subject of much attention recently, due to applications to number theory, geometric group theory, hyperbolic geometry etc. Interest in this area rose significantly after the seminal work of Margulis (the proof of the Oppenheim conjecture) and Ratner (Raghunathan’s conjectures) involving unipotent flows on homogeneous spaces. Later developments were considerably stimulated by applications to Diophantine approximation. I will survey basics of ergodic theory, then specialize to homogeneous dynamics, then highlight connections to number theory. The latter allow one to utilize certain properties of homogeneous flows, such as quantitative non-​divergence or effective equidistribution of unstable leaves, to prove new results in number theory.

Resources

Learning Materials (Links)

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Dynamics on Homogeneous Spaces and New Applications to Number Theory
  • Wed 13:15-15:00 (HG G 19.1)
  • 16.03 Date 13:15-15:00 (HG G 19.2)
2 h weekly

Offered In

  • Doctorate Mathematics (More Information at: )
    • Subject Specialisation (The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.)
      • Graduate School (Official website of the Zurich Graduate School in Mathematics: In addition to the 401-....-DRL course units, adapted versions for doctoral students of the following course units: 263-4400-00L Advanced Graph Algorithms and Optimization 401-3902-21L Network & Integer Optimization: From Theory to Application 401-3904-22L Convex Optimization 401-3629-00L Quantitative Risk Management 401-3652-00L Numerical Methods for Hyperbolic Partial Differential Equations 151-0530-00L Nonlinear Dynamics and Chaos II 227-0434-10L Mathematics of Information 401-4490-22L Topology Optimization of Engineering Systems ... (continued ))