Polynomials vanishing on Cartesian products: The Elekes-Szab\'o Theorem revisited

Orit Raz
Tel Aviv University
Computer Science

I will present the proof of the following statement: Let F be a bounded-degree trivariate real polynomial. Then F vanishes on at most O(n^{11/6}) points of any nxnxn Cartesian product, unless (locally) F has a certain simple form. This improves a result of Elekes-Szab\'o from 2012. This is a joint work with Micha Sharir and Frank de Zeeuw.

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