Expander graph: x connects to x+1 and 1/x modulo a prime number p.

Publications (arxiv.org, Google Scholar)

  1. On bond anisotropy for the Ising model through the Geometry of Numbers. arxiv 2024
  2. Classification and statistics of Cut-and-Project sets. with Yotam Smilansky, Barak Weiss. arxiv
    Journal of the European Mathematical Society 2023 (75 pages)
  3. Effective Intrinsic Ergodicity For Countable State Markov Shifts. with Omri Sarig. arxiv
    Israel Journal of Mathematics 2022
  4. Pressure inequalities for Gibbs measures of countable Markov shifts. arxiv
    Dynamical Systems 2021
  5. Effective counting for discrete lattice orbits in the plane via Eisenstein series. with C. Burrin, A. Nevo, B. Weiss. arxiv
    L'Enseignement Mathématique 2021
  6. Quantitative multiple pointwise convergence and effective multiple correlations. with Ronggang Shi. arxiv
    Journal of Differential Equations 2021
  7. A convexity criterion for unique ergodicity of Interval Exchange transformations. arxiv
    Moscow Journal of Combinatorics and Number Theory 2020
  8. Metric Diophantine approximation with congruence conditions. with Erez Nesharim, Ronggang Shi. arxiv
    International Journal of Number Theory 2020
  9. Effective counting on translation surfaces. with Amos Nevo, Barak Weiss. arxiv
    Advances of Mathematics 2020
  10. Counting saddle connections in a homology class modulo q. with Michael Magee. arxiv
    Journal of Modern Dynamics 2019
  11. A Multiple ergodic theorem. (Appendix) with Ronggang Shi. arxiv
    International Mathematics Research Notices 2019
  12. Variance estimates. (Appendix) with Jayadev S. Athreya. arxiv
    Journal of Modern Dynamics 2019
  13. Distribution of shapes of orthogonal lattices. with Manfred Einsiedler, Philipp Wirth. arxiv
    Ergodic Theory and Dynamical Systems 2019 (73 pages)
  14. Effectivity of uniqueness of the maximal entropy measure on p-adic homogeneous spaces. arxiv
    Ergodic Theory and Dynamical Systems 2016
  15. A badly expanding set on the 2-torus. (Counter-Example to a geometric expansion conjecture) arxiv 2016


  1. Course on Entropy Technion 2020. Course homepage.
  2. Course on Expander graphs Tel Aviv University 2017. Course homepage.


  1. Hecke Tree and CM Points Github.
  2. Ising Model Github.
  3. Lorenz Attractor Github.
  4. Quasicrystal Visualization Github.
  5. Interactive Modular Surface / Space of 2-Lattices Shadertoy.
  6. Hyperbolic Shockwave (Geodesic flow of rational points on a Horocycle) Shadertoy.


  1. Slides on Effective Intrinsic Ergodicity for Countable Markov Shifts link
  2. Detailed Slides on Cut and Project Quasicrystals and Rogers Formula link
  3. Slides on Low Entropy Method. link
  4. Survey on Counting by Smoothing (around the problem addressed in "Effective counting for discrete lattice orbits in the plane via Eisenstein series"). Notes
  5. Notes on Veech's proof of Siegel's formula. link
  6. Notes on Equidistribution on affine symmetric spaces after Eskin-McMullen. link


  1. Translation of Jean-Francois Quint's Bourbaki Notes on Moduli spaces of flat surfaces. link
  2. Translation of "A local criterion for regularity of a system of points. Delone at al". Translated by Karina Samvelyan. link

Oberwolfach Reports

  1. Arbeitsgemeinschaft 2019: Zimmer's Conjecture. Invariance principles. Report (free access)
  2. Arbeitsgemeinschaft 2018: Rigidity of Stationary Measure.Stationary measures on moduli spaces. Report (free access)
  3. Arbeitsgemeinschaft 2012: Ergodic Theory and Combinatorial Number Theory. Green-Tao and Tao-Ziegler Theorems II. Report (free access)


  1. Counting Saddle Connections Here is a lecture of mine on the asymptotics of saddle connections on translation surfaces. Describes collaboration with Claire Burrin, Barak Weiss, Amos Nevo and Michael Magee. Video BIRS.
  2. Cut-and-Project Quasicrystals Lecture about classification cut-and-project quasicrystals and and asymptotics for patches of generic quasicrystals. Describes joint work with Barak Weiss and Yotam Smilansky. Video ICTS (Related) Slides
  3. Counting Saddle Connections Short talk on collaboration with Barak Weiss and Amos Nevo. Video Warwick Notes


Senior Post Doc Weizmann Institute of Science. 2020-2023.
Post Doc Technion. 2018-2020.
Post Doc Tel Aviv University. 2015-2018.
Visit Israel Institute For Advances Studies. Hebrew University of Jerusalem 09/2013-02/2014.
PhD in Mathematics at ETH Zürich. 2011-2015. Doctoral thesis: Some applications of effective unipotent dynamics.
Bsc & Msc in Mathematics at ETH Zürich. 2007-2011. Master thesis: Weak bounds on the asymptotics of the discrete spectrum of ∆ on H/Γ.