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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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Cite

BibTeXRIS
BibTeX
@misc{binyamini2026establishing,
  title = {{Establishing the Polynomial Wolff Axioms for $δ$-Separated $δ$-Tubes With #o-minimality}},
  author = {Gal Binyamini and Yuval Salant},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24135},
  eprint = {2609.24135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24135},
}
RIS
TY  - UNPB
TI  - Establishing the Polynomial Wolff Axioms for δ-Separated δ-Tubes With #o-minimality
AU  - Gal Binyamini
AU  - Yuval Salant
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24135
UR  - https://arxiv.org/abs/2609.24135
AB  - 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.
ER  -