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

Contact

René Rühr
Department of Mathematics
Weizmann Institute
Rehovot, Israel
rene.ruhr@weizmann.ac.il

Publications (arxiv.org, Google Scholar)

Effective Intrinsic Ergodicity For Countable State Markov Shifts.
René Rühr, Omri Sarig.
draft
Classification and statistics of Cut-and-Project sets.
René Rühr, Yotam Smilansky, Barak Weiss.
arxiv. 2020 (65 pages)
arxiv
Effective counting for discrete lattice orbits in the plane via Eisenstein series.
Claire Burrin, Amos Nevo, René Rühr, Barak Weiss.
L'Enseignement Mathématique. 2021.
arxiv journal
Pressure inequalities for Gibbs measures of countable Markov shifts.
Dynamical Systems: An International Journal. 2021.
arxiv journal
Quantitative multiple pointwise convergence and effective multiple correlations.
René Rühr, Ronggang Shi.
Journal of Differential Equations. 2021.
arxiv journal
A convexity criterion for unique ergodicity of Interval Exchange transformations.
Moscow Journal of Combinatorics and Number Theory. 2020
arxiv journal
Metric Diophantine approximation with congruence conditions.
Erez Nesharim, René Rühr, Ronggang Shi.
International Journal of Number Theory. 2020.
arxiv journal
Effective counting on translation surfaces.
Amos Nevo, René Rühr, Barak Weiss.
Advances of Mathematics. 2020.
arxiv journal
Counting saddle connections in a homology class modulo q.
Michael Magee, René Rühr.
Journal of Modern Dynamics. 2019.
arxiv journal
Distribution of shapes of orthogonal lattices.
Manfred Einsiedler, René Rühr, Philipp Wirth.
Ergodic Theory and Dynamical Systems. 2019. (77 pages)
arxiv journal
A Multiple ergodic theorem. (Appendix)
René Rühr, Ronggang Shi.
International Mathematics Research Notices. 2019.
arxiv journal
Variance estimates. (Appendix)
Jayadev S. Athreya, René Rühr.
Journal of Modern Dynamics. 2019.
arxiv journal
Effectivity of uniqueness of the maximal entropy measure on p-adic homogeneous spaces.
Ergodic Theory and Dynamical Systems. 2016.
arxiv journal
A badly expanding set on the 2-torus.
arxiv only. 2016.
arxiv

Software

Interactive Modular Surface / Space of 2-Lattices
GPU Shader. Shadertoy.

Teaching

Course on Expander graphs
Tel Aviv University 2017. Course hompage.
Course on Entropy
Technion 2020. Course hompage.

Videos

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.
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

Oberwolfach Reports

Arbeitsgemeinschaft 2019: Zimmer's Conjecture. Lecture 9: Invariance principles. Report (free access)
Arbeitsgemeinschaft 2018: Rigidity of Stationary Measure. Lecture 21: Stationary measures on moduli spaces. Report (free access)
Arbeitsgemeinschaft 2012: Ergodic Theory and Combinatorial Number Theory. Lecture 27: Green-Tao and Tao-Ziegler Theorems II. Report (free access)

CV

Post Doc Weizmann. Since 2020
Funded by Omri Sarig
Post Doc Technion. 2018-2020
Funded by the ERC Starter grant of Uri Shapira
Post Doc Tel Aviv University. 2015-2018.
Funded by ERC grant of Barak Weiss and an early-post doc stipendium of the Swiss National Science Foundation
PhD in Mathematics at ETH Zürich. 2011-2015.
Doctoral thesis: Some applications of effective unipotent dynamics. Supervised by Manfred Einsiedler.
Bsc & Msc in Mathematics at ETH Zürich. 2007-2011.
Master thesis: Weak bounds on the asymptotics of the discrete spectrum of ∆ on H/Γ. Supervised by Manfred Einsiedler and Uri Shapira.