A Survey of the Kakeya Conjecture, 2000–2025

2025/12/10 by Joshua Zahl, Zahl, Joshua
Mathematics · #Advanced Harmonic Analysis Research #Geometry and complex manifolds #Advanced Banach Space Theory

paper · pdf · doi:10.1137/25m1805965

Abstract

We survey progress on the Kakeya conjecture in Euclidean space, with an emphasis on developments that have occurred since the previous surveys by Wolff and Katz-Tao.

Citations

• Spectral Dimension Flow, Localized Non-Orientable Horizon Defects, and Emergent Time in Black Holes: A Geometry-Driven Effective Framework
• The Assouad dimension of Kakeya sets in ℝ³
• A note on Fourier restriction and nested Polynomial Wolff axioms
• On the multilinear restriction and Kakeya conjectures

Related

• Recent progress on the Kakeya conjecture
• Introduction to the proof of the Kakeya conjecture
• The Kakeya Conjecture: where does it come from and why is it important?
• Generalized Arithmetic Kakeya
• New Kakeya estimates using the polynomial Wolff axioms