Recent progress on the Kakeya conjecture

TL;DR

This survey reviews recent advances in the Kakeya conjecture, highlighting progress made since 1999, particularly on the standard Kakeya problem involving line segments, and discusses recent work by the authors.

Contribution

It provides an updated overview of developments in the Kakeya problem post-1999, including new results by the authors, focusing on the standard line segment variant.

Findings

Summarizes key recent results on Kakeya conjecture

Highlights progress on the standard Kakeya problem since 1999

Includes recent work by the authors on Kakeya estimates

Abstract

The purpose of this article is to survey the developments on the Kakeya problem in recent years, concentrating on the period after the excellent 1999 survey of Wolff, and including some recent work by the authors. We will focus on the standard Kakeya problem for line segments and not discuss other important variants (such as Kakeya estimates for circles, light rays, or $k$-planes).