Mathematics Colloquium

Sticky Kakeya sets in R^3

Speaker: Hong Wang, UCLA

Location: Warren Weaver Hall 1302

Date: Monday, December 12, 2022, 3:45 p.m.


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 the talk, we will also discuss the connection to projection theory in geometric measure theory.