108 citations · 378 across the 31 of their papers we have counts for
33 papers
Structure of cell decompositions in Extremal Szemerédi-Trotter examples
Nets Katz, Olivine Silier
The symmetric case of the Szemerédi-Trotter theorem says that any configuration of lines and points in the plane has at most incidences. We describe a recipe i…
Kakeya sets from lines in
Nets Hawk Katz, Shukun Wu, Joshua Zahl
We prove that every Kakeya set in formed from lines of the form with must have Hausdorff dimension ; Kakeya sets…
A Kakeya maximal function estimate in four dimensions using planebrushes
Nets Hawk Katz, Joshua Zahl
We obtain an improved Kakeya maximal function estimate and improved Kakeya Hausdorff dimension estimate in using a new geometric argument called the planebrush. A pl…
On the discretized sum-product problem
Larry Guth, Nets Hawk Katz, Joshua Zahl
We give a new proof of the discretized ring theorem for sets of real numbers. As a special case, we show that if is a -set in the sense of Katz and…
On the polynomial Wolff axioms
Nets Hawk Katz, Keith M. Rogers
We confirm a conjecture of Guth concerning the maximal number of -tubes, with -separated directions, contained in the -neighborhood of a real algebraic variety. Modulo a f…
An improved bound on the Hausdorff dimension of Besicovitch sets in
Nets Hawk Katz, Joshua Zahl
We prove that any Besicovitch set in must have Hausdorff dimension at least for some small constant . This follows from a more general result about…