Papers and Preprints by Barak Weiss

• w/ Osama Khalil and Manuel Luethi, Measure rigidity and equidistribution for fractal carpets, preprint (2025).

• w/ Alon Agin, The Dirichlet spectrum, preprint (2024).

• w/ Dmitry Kleinbock, Nikolay Moshchevitin and Jacqueline Warren, Singularity, weighted uniform approximation, intersections and rates, preprint (2024).

• w/ Or Ordentlich and Oded Regev, Bounds on the density of smooth lattice coverings, preprint (2023), to appear in Journal d'Analyse.

• w/ John Smillie, Peter Smillie, and Florent Ygouf, Horospherical dynamics in invariant subvarieties, Adv. Math. 451 Article ID 109783, 54 p. (2024).

• w/ Jon Chaika and Florent Ygouf, Horocycle dynamics in rank one invariant subvarieties I: weak measure classification and equidistribution, preprint (2022), to appear in Israel J. Math.

• w/ Pat Hooper and Ferran Valdez, Stellar foliation structures on surfaces, preprint (2023).

• w/ Jon Chaika, On the ergodic properties of the Rel foliation, Forum of Mathematics, Pi 12 paper no. e7, 25pp (2024).

• w/ Uri Shapira, Geometric and arithmetic aspects of approximation vectors, preprint (2022).

• w/ Jon Chaika, The horocycle flow on the moduli space of translation surfaces, International Congress of Mathematicians 2022, Helsinki, Finland, virtual, July 6--14, 2022. Volume 5. Sections 9--11. Berlin: European Mathematical Society (EMS). 3412-3430 (2023).

• w/ Rene Ruehr and Yotam Smilansky, Classification and statistics of cut-and-project sets, J. Eur. Math. Soc. 26 (2024), no. 9, pp. 3575--3638.

• w/ Or Ordentlich and Oded Regev, New bounds on the density of lattice coverings, J. Amer. Math. Soc. 35 (2021), no. 1, 295--308

• w/ Jon Chaika and John Smillie, Tremors and horocycle dynamics on the moduli space of translation surfaces, preprint (2020), updated Nov. 2024.

• w/ Yiftach Dayan and Arijit Ganguly, Random walks on tori and normal numbers in self-similar sets, Amer. J. Math. 146 (2024) no. 2, 467--493.

• w/ Dmitry Kleinbock and Nikolay Moshchevitin, Singular vectors on manifolds and fractals, Israel J. Math. 245 (2021), no. 2, 589--613.

• w/ Alexander Rahm, Noam Solomon and Tara Trauthwein, The distribution of rational numbers on Cantor's middle thirds set, Unif. Distrib. Theory 15 (2020), no. 2, 73--92.

• w/ Faustin Adiceam and Yaar Solomon, Cut-and-project quasicrystals, lattices, and dense forests, J. London Math. Soc. 105 (2022) 1167--1199.

• w/ Claire Burrin, Amos Nevo and Rene Ruehr, Effective counting for discrete lattice orbits in the plane via Eisenstein series, Enseign. Math. 66 (2020), no. 3-4, 259--304.

• w/ Amos Nevo and Rene Ruehr, Effective counting on translation surfaces, Adv. Math. 360 (2020).

• w/ David Simmons, Random walks on homogeneous spaces and diophantine approximation on fractals, Inv. Math. 216 (2019) 337--394.

• w/ Oded Regev and Uri Shapira, Counterexamples to a conjecture of Woods, Duke Math. J. 166 (2017), 2443--2446.

• w/ Matt Bainbridge and John Smillie, Horocycle dynamics: new invariants and eigenform loci in the stratum H(1,1), Memoirs of the AMS 1384 (2022) 100p.

• w/ Simon Kristensen and Steffen Hojris Pedersen, Some remarks on Mahler's classification in higher dimension, Moscow Journal of Combinatorics and Number Theory 6 (2016) 177--190.

• w/ Omri Solan and Yaar Solomon, On problems of Danzer and Gowers and dynamics on the space of closed subsets of R^d, IMRN 21 (2017) 6584--6598.

• w/ Pat Hooper, Rel leaves of the Arnoux-Yoccoz surfaces, with an appendix by Lior Bary-Soroker, Mark Shusterman and Umberto Zannier, Selecta Math., (2018) 24, no. 2, 875-934, erratum (in which we fix an error noted by Florent Ygouf, the main results of the paper remain valid), previous version (genus 3 only).

• w/ Dmitry Kleinbock and Ronggang Shi, Pointwise equidistribution with an error rate and with respect to unbounded functions, Math. Ann. (2016) 1--23.

• w/ Ronggang Shi, Invariant measures for solvable groups and diophantine approximation, Israel J. Math. 219 (2017) 479--505.

• w/ Uri Shapira, A volume estimate for the set of stable lattices, Comptes Rendus Mathematique 352 2014 875--879.

• w/ Samuel Lelièvre and Thierry Monteil, Everything is illuminated, Geometry and Topology 20 (2016), 1737--1762.

• w/ Yaar Solomon, Dense forests and Danzer sets, Annales Scientifique de l'ENS 49 (2016) 1049--1070.

• w/ Michael Levin and Uri Shapira, Closed orbits for the diagonal group and well-rounded lattices, Groups, Geometry and Dynamics 10 (2016) 1211--1225.

• w/ Dmitry Kleinbock, Values of binary quadratic forms at integer points and Schmidt games, in Recent trends in ergodic theory and dynamical systems, 77--92, Cont. Math. 631 (2015).

• w/ Uri Shapira, Stable lattices and the diagonal group, J. Eur. Math. Soc. 18 (2016) 1753--1767, original version (expanded).

• w/ Erez Nesharim, Bad(i,j) is absolutely winning on C, appendix to the paper Badly approximable vectors on a vertical Cantor set by Erez Nesharim, Moscow J. of Comb. and Number Th. 3 (2013) 88-116.

• w/ Samuel Lelièvre, Translation surfaces with no convex presentation, GAFA 25 1902--1936 (2015).

• w/ Uri Shapira, On the Mordell-Gruber spectrum, Int. Math. Res. Not. IMRN 14 5518--5559 (2015).

• w/ Alan Haynes and Mike Kelly, Equivalence relations on separated nets arising from linear toral flows, Proc. Lond. Math. Soc. (3) 109 (2014), no. 5, 1203--1228 (updated Jan. 2015).

• w/ Jinpeng An, Remarks on minimal sets and conjectures Cassels, Swinnerton-Dyer and Margulis, Moscow J. of Comb. and Number Th. 3 (2013) 24--43.

• w/ Yair Minsky, Cohomology classes represented by measured foliations, and Mahler's question for interval exchange transformations, Annales scientifiques de l'ENS 2 (2014) 245--284.

• w/ Uri Bader, Alex Furman and Alex Gorodnik, Rigidity of group actions on homogeneous spaces, III Duke Math. J. 164 (2015), no. 1, 115--155.

• w/ Dmitry Kleinbock, Modified Schmidt games and a conjecture of Margulis, J. Mod. Dyn. 7 (2013) 429-460.

• w/ Pascal Hubert, Ergodicity for infinite periodic translation surfaces, Compositio Math. 149 (2013) 1364-1380.

• w/ Pat Hooper, Generalized staircases: recurrence and symmetry, Annales de L'Institut Fourier 62 (2012) 1581-1600.

• w/ Pat Hooper and Pascal Hubert, Dynamics on the infinite staircase surface, Dis. Cont. Dyn. Sys. 33 (2013) 4341-4347.

• w/ Meital Cohen, Parking garages with optimal dynamics, Geom. Dedicata 161 (2012) 157-167.

• w/ François Maucourant, Lattice actions on the plane revisited, Geometriae Dedicata, 157 (2012) 1-21.

• w/ Ryan Broderick, Lior Fishman, Dmitry Kleinbock and Asaf Reich, The set of badly approximable vectors is strongly C^1 incompressible, Math. Proc. Cambridge Phil. Soc. 153 (2012) 319-339.

• w/ Ryan Broderick, Yann Bugeaud, Lior Fishman and Dmitry Kleinbock, Schmidt's game, fractals, and numbers normal to no base, Math. Res. Lett. 17 (2010), no. 2, 307-321.

• w/ Dmitry Kleinbock, Modified Schmidt games and diophantine approximation with weights, Adv. Math. 223 (2010), 1276-1298.

• w/ John Smillie, Characterizations of lattice surfaces, Inv. Math. 180 (2010), no. 3, 535-557.

• w/ John Smillie, Finiteness results for flat surfaces: large cusps and short geodesics, Comm. Math. Helv. 85 (2010) 313-336.

• w/ John Smillie, Veech's dichotomy and the lattice property, Ergodic Theory Dyn. Syst. 28 (2008) 1959-1972.

• w/ Dmitry Kleinbock, Dirichlet's theorem on diophantine approximation and homogeneous flows, J. Mod. Dyn. 2 (2008) 43-62.

• w/ Alex Gorodnik, Distribution of lattice orbits on homogeneous varieties, Geom. Funct. Anal. 17 (2007), no. 1, 58-115.

• w/ John Smillie, Finiteness results for flat surfaces: a survey and problem list, (2006) in Partially hyperbolic dynamics, laminations, and Teichmüller flow (Proceedings of a conference, Fields Institute, Toronto Jan 2006), G. Forni (ed.)

• Divergent trajectories and Q-rank, Israel J. Math. 152 (2006), 221-227.

• w/ Dmitry Kleinbock, Friendly measures, homogeneous flows, and singular vectors, in Algebraic and Topological Dynamics, S. Kolyada, Y. Manin and T. Ward, eds, Cont. Math. 385 (2005).

• w/ Dmitry Kleinbock, Badly approximable vectors on fractals, Probability in mathematics, Israel J. Math. (special volume in honor of Hillel Furstenberg). 149 (2005), 137-170.

• w/ Dmitry Kleinbock and Elon Lindenstrauss, On fractal measures and diophantine approximation, Selecta Math. (N.S.) 10 (2004), no. 4, 479-523.
• Divergent trajectories on noncompact parameter spaces, Geom. Funct. Anal. 14 (2004), no. 1, 94-149.
• w/ Dmitry Kleinbock, Bounded geodesics in moduli space, Int. Math. Res. Not. 30 (2004), 1551-1560.

• w/ John Smillie, Minimal sets for flows on moduli space, Israel J. Math. 142 (2004), 249-260.

• w/ George Tomanov, Closed orbits for actions of maximal tori on homogeneous spaces, Duke Math. J. 199 no. 2 (2003) 367-392.
• w/ Yair N. Minsky, Non-divergence of horocyclic flows on moduli spaces, J. Reine Angew. Math. 552 (2002) 131-177.
• Dynamics on parameter spaces: submanifold and fractal subset questions, in Rigidity in Dynamics and Geometry, M. Burger and A. Iozzi, eds, 425-440. Springer (2002).
• w/ Elon Lindenstrauss, On sets invariant under the action of the diagonal group, Ergodic Theory Dynam. Systems 21 (2001), no. 5, 1481-1500.
• Almost no points on a Cantor set are very well approximable, Proc. R. Soc. Lond. A (2001) 457 949-952.
• Unique ergodicity on compact homogeneous spaces, Proc. AMS 129, 2 (2001) 585-592.
• w/ Nimish A. Shah, On actions of epimorphic subgroups on homogeneous spaces, Ergodic Theory and Dynamical Systems 20, 2 (2000) 567-592.
• w/ Shahar Mozes, Minimality and unique ergodicity for subgroup actions, Annales de l'Institut Fourier 48, 5 (1998) 1533-1541.
• Finite dimensional representations and subgroup actions on homogeneous spaces, Israel Journal of Mathematics, 106 (1998), 189-207.
• w/ Alexander Barabasch and Aviezri Fraenkel Iterated Beatty sequences, Random and Computational Dynamics 6 (1993).