PDE/Analysis Seminar

Tuesday, December 13, 2022 at 4:00pm

Building 2, 2-136
182 MEMORIAL DR, Cambridge, MA 02139

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

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