A Survey of the Kakeya conjecture, 2000-2025
Joshua Zahl
TL;DR
This survey reviews recent progress on the Kakeya conjecture in Euclidean space from 2000 to 2025, highlighting developments since earlier surveys by Wolff and Katz-Tao.
Contribution
It compiles and analyzes the latest advancements and research trends related to the Kakeya conjecture over the past 25 years.
Findings
Significant progress in understanding Kakeya sets and their dimensions.
New techniques and bounds have been developed since prior surveys.
Open problems and future directions are identified.
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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Geometry and complex manifolds · Advanced Banach Space Theory