##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Hong Wang

#### UCLA

## Sticky Kakeya sets in R^3

##### Abstract:

A Kakeya set is a set of points in R^n which contains a unit line segment in every direction. The Kakeya conjecture states that the dimension of any Kakeya set is n. This conjecture remains wide open for all n \geq 3.

Together with Josh Zahl, we study a special collection of the Kakeya sets, namely the sticky Kakeya sets, where the line segments in nearby directions stay close. We prove that sticky Kakeya sets in R^3 have dimension 3. In this talk, we will discuss background of the problem and its connection to analysis, combinatorics, and geometric measure theory.

Ioan Bejenaru

### May 4, 2023

### 4:00 PM

APM 6402

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