Publications

Online talks:

  1. On a weird rational average (Hebrew) – Technion math faculty, Math club:
    abstract The “wrong” way to sum up two rationals is by taking \frac{a}{b} \oplus \frac{c}{d} := \frac{a+c}{b+d}. However, while this doesn’t really give us the sum of the rational, it is an interesting operation nonetheless called the “mediant”. In this lecture we will learn about this mediant and its properties, and its see some of its many connection all sorts of interesting mathematics.
  2. From white noise to natural noise (Hebrew) – Technion math faculty:
    abstract One of the fascinating problems in computer graphics is making objects look as real as possible, starting from clouds and mountains, and up to skin and hair. It was known already from the beginning that some random white noise can help this feeling of “realness”, but this help has its limit too. In this lecture we will see how people created this white noise, and combined it with some interesting mathematics, in order to create the “natural” noise which is used today almost everywhere from computer games to Hollywood moives.
  3. The structure behind Apery’s proof – CUNY math faculty, Number theory seminar:
    abstract In 1978, Apéry proved the irrationality of the Riemann zeta value \zeta(3) by utilizing a fast converging sequence of rational approximations. However, the details of his proof remained difficult to comprehend. Since then, many mathematicians have attempted to either elucidate Apéry’s approach or seek out new proofs altogether. Inspired by computer algorithms to find such approximations, an idea about a hidden mathematical structure behind the proof was beginning to formalize. This structure, which we call the conservative matrix field, not only clarifies some of Apéry’s proof but also offers a framework for Apéry-like irrationality proofs and relates them to the broader themes of number theory and dynamics. In this talk, we will explore the properties of the conservative matrix field and discuss how it can be hopefully applied to prove irrationality for other mathematical constants. This research was done as part of the work in the Ramanujan Machine group at the Technion.

Number Theory and Dynamics:

  1. O. David, T. Kim, R. Mor, U. Shapira
    “On the rate of convergence of continued fraction statistics of random rationals“,
    Selecta Mathematica, Volume 31, March 2025, Pages 1-22
    arXiv: arxiv:2401.15586
  2. O. David, U. Shapira,
    “Equidistribution of divergent orbits of the diagonal group in the space of lattices“,
    Ergodic Theory and Dynamical Systems, September 2018
    DOI: 10.1017/etds.2018.80, arXiv: arXiv:1710.05242 [math.DS]
  3. O. David, U. Shapira,
    “Equidistribution of divergent orbits and continued fraction expansion of rationals“,
    London Mathematical Society, Volume 98 (1), August 2018, Pages 149-176
    DOI: 10.1112/jlms.12128, arXiv: arXiv:1707.00427 [math.DS]
  4. O. David, U. Shapira,
    “Dirichlet shapes of unit lattices and escape of mass“,
    International Mathematics Research Notices (January 2017): rnw324.
    DOI: 10.1093/imrn/rnw324, arXiv: arXiv:1607.04048 [math.NT]
  5. O. David, “Shearing in the space of adelic lattices“
    arXiv: arXiv:1909.00053 [math.DS]
  6. O. David, “Local to global property in free groups“
    arXiv: arXiv:1907.05968 [math.GR]
  7. O. David, “Graphs with large girth and free groups“
    arXiv: arXiv:1907.06936 [math.GR]

Statistical Learning:

  1. O. David, S. Moran, A. Yehudayoff,
    “On statistical learning via the lens of compression”,
    NIPS 2016.
    arXiv: arXiv:1610.03592 [cs.LG]

Polynomial Identities:

  1. O. David,
    “The center of the generic G-crossed product“,
    Journal of Algebra, Volume 463, October 2016, Pages 103-133.
    DOI: 10.1016/j.jalgebra.2016.06.017, arXiv: arXiv:1401.4717 [math.RA]
  2. E. Aljadeff, O. David,
    “On regular G-gradings“, 
    Transactions of the American Mathematical Society, Volume 367 (6), June 2015, Pages 4207-4233.
    DOI: 10.1090/S0002-9947-2014-06200-4, arXiv: arXiv:1212.0343 [math.RA]
  3. E. Aljadeff, O. David,
    “On group gradings on PI-algebra“,
    Journal of Algebra, Volume 428, April 2015, Pages 403-424.
    DOI: 10.1016/j.jalgebra.2014.12.042, arXiv: arXiv:1403.0200 [math.RA]
  4. O. David,
    “Graded embeddings of finite dimensional simple graded algebras“,
    Journal of Algebra, Volume 367, October 2012, Pages 120-141.
    DOI: 10.1016/j.jalgebra.2012.06.005 , arXiv: arXiv:1112.5492 [math.RA]

Ramanujan Machine

This research was done as part of my work with the Ramanujan Machine group at the Technion.

  1. M. Shalyt, U. Seligmann, I. Beit Halachmi, O. David, R. Elimelech, I. Kaminer,
    “Unsupervised discovery of formulas for mathematical constants”,
    Advances in Neural Information Processing Systems, Volume 37, 2024
    arXiv: arXiv:2412.16818 [cs.AI]
  2. R. Elimelech, O. David, C. De La Cruz, R. Kalish, W. Berndt, M. Shalyt, M.Silberstein, Y. Hadad, I. Kaminer,
    “Algorithm-assisted discovery of an intrinsic order among mathematical constants”,
    PNAS 2024.
    DOI: 10.1073/pnas.2321440121 , arXiv: arXiv:2308.11829 [cs.AI]
  3. O. Razon, Y. Harris, S. Gottlieb, D. Carmon, O. David, I Kaminer,
    “Automated search for conjectures on mathematical constants using analysis of integer sequences”,
    ICML 2023.
    arXiv: arXiv: 2212.09470 [math.NT]
  4. O. David, “The conservative matrix field“
    arXiv: arXiv:2303.09318
    See also here and here for a short online description.
  5. O. David, “On Euler polynomial continued fractions“
    arXiv: arxiv:2308.02567
    See also here for a short online description.

M.Sc. Thesis: On Regular Gradings of Algebras 

See Also: Google Scholar Page and arXiv page.