Josh Zha

UBC

November 03, 2016 - 4:00 pm , BH 217
Abstract
Trilinear and linear Kakeya-type bounds in R4

A Besicovich set is a compact subset of R^dthatcontains a unit line segment pointing in every direction. The Kakeya conjecture asserts that every Besicovich set in R^d musthave dimensiond. I will discuss some new trilinear Kakeya-typebounds in R⁴, and how these bounds can be used to obtainimproved bounds on the dimension of certain sets in R⁴ thatresemble Kakeya sets. This is joint work with Larry Guth.