O. Raz

activity

20132025

most citedPolynomials vanishing on Cartesian products: The Elekes-Szabó Theorem revisited

45 citations · 119 across the 21 of their papers we have counts for

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Showing 2016Show all

4 papers · 1 filter

math.LO2016

An o-minimal Szemerédi-Trotter theorem

Saugata Basu, Orit E. Raz

We prove an analog of the Szemerédi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field $R$ . One ne…

math.CO2016

Configurations of lines in space and combinatorial rigidity

Orit E. Raz

Let $L$ be a sequence $(ℓ_{1}, ℓ_{2}, \dots, ℓ_{n})$ of $n$ lines in $C^{3}$ . We define the {\it intersection graph} $G_{L} = ([n], E)$ of $L$ , where $[n] := {1, \dots, n}$ , and…

math.CO2016

The Elekes-Szabó Theorem in four dimensions

Orit E. Raz, Micha Sharir, Frank de Zeeuw

Let $F \in C [x, y, s, t]$ be an irreducible constant-degree polynomial, and let $A, B, C, D \subset C$ be finite sets of size $n$ . We show that $F$ vanishes on at most $O(n…

math.MG2016★ 4 cited

A note on distinct distances

Orit E. Raz

We show that, for a constant-degree algebraic curve $γ$ in $R^{D}$ , every set of $n$ points on $γ$ spans at least $Ω (n^{4/3})$ distinct distances, unless $γ$ is an {\it alge…