Title: Kakeya sets in R^3
Abstract: A Kakeya set is a compact subset of R^n that contains a unit line segment pointing in every direction. Kakeya set conjecture asserts that every Kakeya set has Minkowski and Hausdorff dimension n. We prove this conjecture in R^3 as a consequence of a more general statement about union of tubes. We will also discuss the connection to projection theorems in geometric measure theory.
This is joint work with Josh Zahl.
