Papers

  1. On Sarnak's Density Conjecture and its Applications, with Amitay Kamber
    ArXiv
  2. Graphical Designs and Extremal Combinatorics
    Linear Algebra and its Applications (2020) link ArXiv
  3. On periodic sets avoiding given distance on the hyperbolic plane
    ArXiv
  4. Cutoff on Graphs and the Sarnak-Xue Density of Eigenvalues, with Amitay Kamber
    ArXiv
  5. A high-dimensional Hoffman bound and application to problems in extremal combinatorics,
    with Yuval Filmus and Noam Lifshitz, ArXiv
  6. Direct Sum Testing: the General Case, with Irit Dinur
    International Conference on Randomization and Computation, RANDOM2019 link ArXiv ECCC
  7. Cutoff on hyperbolic surfaces, with Amitay Kamber
    Geometriae Dedicata (2019) link ArXiv
  8. Lower bounds for the measurable chromatic number of the hyperbolic plane, with Evan DeCorte
    Discrete & Computational Geometry (2018) link ArXiv
  9. Mixing properties and the chromatic number of Ramanujan complexes
    with Shai Evra and Alex Lubotzky
    IMRN, 2015 (22), pp. 11520-11548 link ArXiv
  10. Spectrum and combinatorics of Ramanujan two-dimensional complexes, with Ori Parzanchevski
    The Israel Journal of Mathematics (2019) link ArXiv
  11. On the chromatic number of a simplicial complex
    Combinatorica (2016) link ArXiv
  12. Dessins d’enfants of valency three and Cayley graphs,
    Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, Vol. 67, No. 2, pp. 46 – 49, 2013 link
  13. A Differential Equation on the Cover Function of the Hexagonal Lattice by the Trivalent Tree,
    Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 6, pp. 91 – 94, 2013 link

Questions I want to see solved:

  1. The chromatic number of the hyperbolic plane. Given a forbidden distance d, what is the minimal number of colors needed in order to color the points of the hyperbolic plane in such a way that no two points at distance d are of the same color? Known results: an upper bound -- linear in d (K'13, PP'17), a lower bound -- 6 for d large enough (DG'19).
  2. A Hoffman bound for cube complexes. The Hoffman bound is a spectral upper bound on the size of an independent set in a graph. Several generalizations of it to simplicial complexes and hypergraphs have been proved recently (G'16, BGP'19, FGL'20). One possible application is this problem (AKS'07,OS'13): how large can a subset of vertices of a binary n-cube be if it does not contain a d-cube?
  3. Probability of return on the hyperbolic plane. The dicsrete random walk with steps of length 1 on the Euclidean plane returns to the ball of radius 1 around the starting point at step n with probability 1/(n+1). Proved by Rayleigh, see B'13 for a 2-page proof. What about the discrete random walk with steps of length d on the hyperbolic plane?
  4. Fourier-Analytical proof of the Square in a Cube test. In DG'19, a 4-query test for checking whether a d-dimensional binary tensor is a tensor product of d binary vectors is introduced (Square in a Cube test). One of the key ingridients of the proof is the BLR linearity test. The BLR test admits an elegant Fourier-analytical proof. Is there such a proof for the Square in a Cube test?

Students

Seminars

At ETH: in Mar 2020, I accidently founded the Online Geometry Seminar, which is currently being organized by Matt Cordes, Francesco Fournier Facio, and myself.

At Bar-Ilan University: together with Tali Kaufman and Uzi Vishne I organized the "Representation Theory and Combinatorics" Research Seminar in Fall 2016 and Sring 2017.

At the Hebrew University: I served as the administrative organizer for Amitsur Algebra Seminar since Spring 2013 until Fall 2015.

Teaching

ETH Zürich
Lecturer for Expanders, Property Testing and Coding, Spring 2019.
Bar-Ilan University
Lecturer for Discrete Mathematics II (83118-2), Spring 2018.
The Hebrew University
Teaching Assistant for:
Discrete Mathematics for Sciences (80187), Fall 2014 and Fall 2015
Calculus II (80132), Spring 2015
Calculus for Sciences (80177), Spring 2014
Linear Algebra I (80134), Fall 2013

Talks

  1. International Laboratory of Algebraic Topology and Its Applications, HSE, Moscow, May 2020
    High-Dimensional Expanders (online talk).
  2. U of Neuchatel Colloquium, Apr 2020
    postponed.
  3. Geometry Graduate Colloquiumg, ETH Zurich, Mar 2020
    postponed.
  4. Zurich Graduate Colloquium, ETH Zurich, Apr 2020
    postponed.
  5. MPS Conference on High-Dimensional Expanders, Simons Foundation, NYC, Oct 2019
    The Vertex Shadow on the Edge Laplacian Spectrum.
  6. Joint Analysis & Combinatorics Seminar, U of Cologne, Oct 2019
    On the chromatic number of the hyperbolic plane.
  7. RANDOM 2019, MIT, Sep 2019
    Direct Sum Testing: the General Case.
  8. Joint Analysis & Combinatorics Seminar, Yale, Sep 2019
    Independent sets and spectral method.
  9. 2 lecture mini-course, U of Neuchatel, Jun 2019
    High-Dimensional Expanders.
  10. 2 lecture mini-course, U of Neuchatel, Mar 2019
    Spectral Methods on Graphs and Surfaces.
  11. goMath Flash Talks, ETH, Zürich, Mar 2019
    Tensor Product Testing.
  12. ETHZ Geometry Seminar, Zürich, Oct 2018
    Spectral Methods: from hyperbolic surfaces to graphs and back.
  13. Student Combinatorics Day at Bar-Ilan U, Ramat Gan, Jul 2018
    Tensor power testing.
  14. U of Haifa Algebra Seminar, Haifa, May 2018
    Density theorems and almost diameter in quotient spaces.
  15. Action Now Wandering Seminar, Technion, Haifa, May 2018
    Density theorems and almost diameter in quotient spaces.
  16. Conference on High Dimensional Combinatorics at IIAS, Jerusalem, April 2018
    On Colorings and Independence. YouTube video
  17. Bar-Ilan U Algebra Seminar, Ramat Gan, Jan 2018
    Cutoff on Hyperbolic Surfaces.
  18. Field Arithmetics Seminar at Tel-Aviv University, Tel-Aviv, Nov 2017
    Spectral Methods: from hyperbolic surfaces to graphs and back.
  19. Bar-Ilan U Combinatorics Seminar, Ramat Gan, Nov 2017
    Spectral Methods: from hyperbolic surfaces to graphs and back.
  20. Technion Algebra Seminar, Haifa, Nov 2017
    Spectral Methods: from hyperbolic surfaces to graphs and back.
  21. Adult mathematics around dessins d'enfants. International conference dedicated to the 65th anniversary of G.B. Shabat, Moscow, May 2017
    Chromatic numbers of Riemannian surfaces [in Russian]. Video.
  22. Applied and Random Topology Seminar, Technion, Haifa, Dec 2016
    Spectral Bounds on the Chromatic Number and Expansion of a Hypergraph
  23. Amitsur Algebra Seminar,Hebrew U, Jerusalem, 21 Apr 2016
    Spectral approach to the chromatic number of a simplicial complex [Thesis Defense Lecture]
  24. Nathan Keller Evening Seminar, Bar-Ilan U, Ramat Gan, March 2016
    Spectral bounds on the chromatic number of graphs and hypergraphs.
  25. Bar-Ilan U Combinatorics Seminar, Ramat Gan, March 2016
    Mixing, Coloring and Expansion of Ramanujan Complexes.
  26. Technion Algebra Seminar, Haifa, Jan 2016
    Mixing, Coloring and Expansion of Ramanujan Complexes.
  27. Combinatorics Seminar at The Tel-Aviv University, Tel-Aviv, Dec 2015
    Simplicial Complexes of High Chromatic Number.
  28. Coloring Graphs Conference at Technion, Haifa, Jul 2015
    Ramanujan complexes: simplicial complexes of large chromatic number.
  29. Math Colloquium at the at Hebrew University, Jerusalem, May 2015
    On the chromatic number of a simplicial complex. (Zuchovitsky Prize Lecture.)
  30. Groups and Geometry Seminar at the University of Geneva, Geneva, Mar 2015
    The chromatic number of Ramanujan complexes.
  31. Combinatorics seminar at the Renyi Institute, Budapest, Oct 2013
    The chromatic number of a simplicial complex.
  32. Lomonosov-2012 at Moscow State University, Moscow, Apr 2012
    Commutative monoid structure o the set of Belyi functions of 3-regular toric dessins d'enfants.
  33. Lomonosov-2011 at Moscow State University, Moscow, Apr 2011
    Cayley graphs and problem of words in one class of finite groups. (Prize for the best talk.)
  34. Amitsur algebra seminar at The Hebrew University, Jerusalem, Oct 2010
    Cayley graphs and dessins d'enfants.
  35. Lomonosov-2010 at Moscow State University, Moscow, Apr 2010
    On duality of Cayley graphs and dessins d'enfants.
  36. 7th International Algebraic conference in Ukraine, Kharkov, Aug 2009
    Cayley graphs, dessins d'enfants and modular curves.