January 30, 2020
|Nets Katz, Caltech|
Planebrushes and the Kakeya problem in 4 dimensions
In work with Josh Zahl, we improve the previous bound by Guth and Zahl on Kakeya sets in 4 dimensions. The main new ingredient is an estimate on planebrushes. These are a generalization on Tom Wolff's hairbrushes which consist of all the tubes which intersect a given 2-plane. Time permitting, I will discuss generalizations to higher dimensions.