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arXiv · 2609.24135

Establishing the Polynomial Wolff Axioms for $δ$-Separated $δ$-Tubes With #o-minimality

Gal Binyamini·Yuval Salant
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Abstract

We establish the full version of a conjecture of Guth and Zahl, giving a lower bound for the volume of a semialgebraic set that has a large intersection with a collection of $δ$-separated $δ$-tubes. Our proof uses o-minimal methods to simplify the proof of Katz and Rogers, who proved the conjecture up to a small factor. We also establish that the constants depend polynomially on the complexity of the semialgebraic set, and more generally in the #o-minimal setting.

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Gal Binyamini, Yuval Salant. 2026-09-21. Establishing the Polynomial Wolff Axioms for $δ$-Separated $δ$-Tubes With #o-minimality. https://arxiv.org/abs/2609.24135

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