Summer Schools

Winter School on Homogeneous Dynamics

Time:Jan. 22- Jan.26, 2024

Venue:SCMS, Fudan University




(Deadline: Nov. 30th)



1. Manfred Einsiedler (Professor, ETH Zurich)

Title: Totally geodesic submanifolds and arithmeticity

Abstract: In this mini course we will discuss the recent theorem of Bader-Fisher-Miller-Stover concerning arithmeticity for hyperbolic manifolds: As conjectured by Reid and McMullen a hyperbolic manifold is arithmetic if and only if there are infinitely many maximal proper totally geodesic submanifolds. This gives a striking connection between the geometry of hyperbolic manifolds and number theory. Moreover the proof uses among other things a crucial input from homogeneous dynamics. We first outline the overall proof structure and then will spend some time discussing the various ingredients.

2. Barak Weiss (Professor, Tel Aviv University)

     Title: Random walks on homogeneous spaces, and Diophantine approximation on fractals

     Abstract: In the last two decades, following breakthrough work of Bourgain-Furman-Lindenstrauss-Mozes and Benoist-Quint, followed by work of Eskin-Mirzakhani, there has been great progress in understanding random walks on homogeneous spaces, and on other related spaces. In work of Simmons-Weiss, Cert-Prohaska-Shi, Dayan-Ganguly-Weiss and forthcoming work of Khalil-Luethi-Weiss, this dynamical input has been used to understand number-theoretic properties of typical points on certain sufficiently regular fractals. I will survey this work, focusing on two main points:

  •   the link between random walks, and number theory;

  •   the main dynamical ideas for analyzing random walks. Specifically, I will give an outline of the exponential drift approach  of Benoist and Quint in the simplest interesting case.


Weixiao Shen

Ronggang Shi 


If you need assistance to apply Chinese Visa, please contact Miss Xue.

Financial Support

The accommodation during the winter school will be arranged and covered by Fudan University. If you need to apply supports for the travel, please send an email to Miss.Xue (


Jan. 22 registration; Jan 23-26 Lectures

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