Orit Raz

I am a senior lecturer at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem, Jerusalem, Israel.
For the school year 2024/25, I am also a Member at the Institute for Advanced Study in Princeton, NJ.

Before that I was a Postdoctoral Fellow at the University of British Columbia, Vancouver, B.C., Canada.
Before that, I was a Member at the Institute for Advanced Study, Princeton, New Jersey.
Before that, I received my PhD from Tel-Aviv University, under the supervision of Prof. Micha Sharir.



Contact

Office: Manchester Bldg. 004
E-mail: oritraz [at] mail.huji.ac.il

Einstein Institute of Mathematics, Hebrew University,
Givat Ram, Jerusalem 91904, Israel.



Students

  • Hadas Baer-Erenfeld (2021-22)
  • Yaara Jahn (2024-current)

    Teaching

    Introduction to Combinatorial Geometry (2023-24), Discrete Mathematics (2019-20, 2021-22, 2023-24), Seminar on Methods in Combinatorial Geom- etry (2019-20), Combinatorics (2020-21), Seminar on Combinatorial Geometry (2020-21), Seminar on Graph rigidity (2020-21).



    Recent Papers

    S. Artstein-Avidan and O. Raz,
    Weighted covering numbers of convex sets,
    Adv. Math., 227 (2011): 730--744.

    O. E. Raz,
    On the zone of the boundary of a convex body,
    Comput. Geom. Theory Appls., 48 (2015): 333--341.

    O. E. Raz, M. Sharir, and J. Solymosi,
    On triple intersections of three families of unit circles,
    Discrete Comput. Geom., 54 (2015): 930--953.

    O. E. Raz, O. Roche-Newton and M. Sharir
    Sets with few distinct distances do not have heavy lines
    Discrete Math., 338 (2015): 1484--1492.

    O. E. Raz, M. Sharir and J. Solymosi,
    Polynomials vanishing on grids: The Elekes-R\`onyai problem revisited,
    Amer. J. Math., 138.4 (2016): 1029--1065.

    O. E. Raz, M. Sharir, and F. de Zeeuw
    Polynomials vanishing on Cartesian products: The Elekes-Szab\'o Theorem revisited,
    2015, Duke Math. J., 165 (18) (2016): 3517--3566.

    O. E. Raz and M. Sharir,
    Unit-area triangles: Theme and variation,
    2015, Combinatorica, 37.6 (2017) 1221--1240.

    O. E. Raz, M. Sharir, and I. D. Shkredov,
    On the number of unit-area triangles spanned by convex grids in the plane,
    2016, Comput. Gepm. Theory Appls., 62 (2017), 25--33.

    O. E. Raz,
    Configurations of lines in space and rigidity of planar structures,
    Discrete Comput. Geom. (special issue), 58.4 (2017), 986--1009.

    R. Ben Avraham, M. Henzez, R. Jaumez, B. Keszeghx, O. E. Raz, M. Sharir, and I. Tubis,
    Minimum partial matching and Hausdorff RMS-distance under translation: Combinatorics and algorithms,
    2016, Algorithmica 80.8 (2018), 2400--2421.

    O. E. Raz, M. Sharir, and F. de Zeeuw
    The Elekes-Szab\'o Theorem in four dimensions,
    Israel J. Math., 227 (2018), 663--690.

    S. Basu and O. E. Raz,
    An o-minimal Szemer\'edi-Trotter theorem,
    Q. J. Math., 69 (2018), 223--239.

    O. E. Raz and A. Wigderson,
    Subspace arrangements, graph rigidity and derandomization through submodular optimization,
    2019, Building Bridges II. On the occasion of the 70th birthday of Laszlo Lovasz.

    O. E. Raz,
    A note on distinct distances,
    Combinat. Probab. Comput. , 29.5 (2020), 650--663..

    O. E. Raz and Z. Shem-Tov
    Expanding polynomials: A generalization of the Elekes-Ronyai theorem to d variables ,
    Combinatorica 40.5 (2020), 721--748.

    E. Ezra, O. E. Raz, M. Sharir, J. Zahl
    Counting and cutting rich lenses in arrangements of circles,
    SIAM J. Discrete Math, 36.2 (2022), 958--974.

    O. E. Raz and J. Solymosi
    Dense graphs have rigid parts ,
    Discrete Comput. Geom., 69.4 (2023), 1079--1094.

    A. Lew, E. Nevo, Y. Peled, and O. E. Raz
    Sharp threshold for rigidity of random graphs
    Bull. London Math. Soc., 55 (2023), 490--501.

    A. Lew, E. Nevo, Y. Peled, and O. E. Raz
    On the d-dimensional algebraic connectivity of graphs,
    Israel J. Math., 256 (2023), 479--511.

    O. E. Raz and J. Zahl
    On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Ronyai theorem
    Geom. Funct. Anal. 34 (2024), 209--262.

    H. Baer-Erenfeld and O. E. Raz
    Distinct distances for points lying on curves in R^d---the bipartite case
    Submitted.
    Also in arXiv:2304.06812.

    A. Lew, E. Nevo, Y. Peled, and O. E. Raz
    Rigidity expander graphs
    Submitted.
    Also in arXiv:2304.01306.

    Publications in Proceedings of Conferences

    O. E. Raz, M. Sharir and J. Solymosi,
    Polynomials vanishing on grids: The Elekes-R\`onyai problem revisited,
    Proc. 30th Annu. Sympos. Comput. Geom., 2014, 251--260.

    O. E. Raz, M. Sharir and J. Solymosi,
    On triple intersections of three families of unit circles,
    Proc. 30th Annu. Sympos. Comput. Geom., 2014, 198--205.

    R. Ben Avraham, M. Henzez, R. Jaumez, B. Keszeghx, O. E. Raz, M. Sharir, and I. Tubis,
    Minimum partial matching and Hausdorff RMS-distance under translation: Combinatorics and algorithms,
    Proc. 22nd European Sympos. Algorithms, 2014, 100--111.

    O. E. Raz, M. Sharir, and F. de Zeeuw
    Polynomials vanishing on Cartesian products: The Elekes-Szab\'o Theorem revisited,
    Proc. 31st Annu. Sympos. Comput. Geom., 2015, 522--536.

    O. E. Raz and M. Sharir,
    The number of unit-area triangles in the plane: Theme and variations,
    Proc. 31st Annu. Sympos. Comput. Geom., 2015, 522--536.

    O. E. Raz,
    Configurations of lines in space and combinatorial rigidity,
    Proc. 32nd Annu. Sympos. Comput. Geom., 2016, 58:1--58:14.
    (Invited to special issue.)

    O. E. Raz and J. Solymosi
    Every embedding of a dense graph has a rigid subset
    Proc. 36th Annu. Sympos. Comput. Geom., 2020, 65:1--65:13.

    E. Ezra, O. E. Raz, M. Sharir, J. Zahl,
    On rich lenses in planar arrangements of circles and related problems
    Proc. 37th Annu. Sympos. Comput. Geom., 2021, 35:1--35:15.