PDE/Analysis Seminar

Featured Speaker: Hong Wang (UCLA)

Title: Stick Kakeya sets in $R^3$

Abstract:  A Kakeya set is a set of points in $\mathbb{R}^n$ 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 $\mathbb{R}^3$ have dimension 3. In the talk, we will also discuss the connection to projection theory in geometric measure theory