Joshua Zahl

activity

20062026

most citedSpectral gaps, additive energy, and a fractal uncertainty principle

46 citations · 441 across the 46 of their papers we have counts for

collaborators

Showing 2017Show all

3 papers · 1 filter

math.MG2017★ 23 cited

Breaking the 3/2 barrier for unit distances in three dimensions

Joshua Zahl

We prove that every set of $n$ points in $R^{3}$ spans $O (n^{295/197 + ε})$ unit distances. This is an improvement over the previous bound of $O (n^{3/2})$ . A key ingredient in…

math.CA2017★ 24 cited

An improved bound on the Hausdorff dimension of Besicovitch sets in $R^{3}$

Nets Hawk Katz, Joshua Zahl

We prove that any Besicovitch set in $R^{3}$ must have Hausdorff dimension at least $5/2 + ε_{0}$ for some small constant $ε_{0} > 0$ . This follows from a more general result about…

math.CA2017★ 29 cited

Polynomial Wolff axioms and Kakeya-type estimates in $R^{4}$

Larry Guth, Joshua Zahl

We establish new linear and trilinear bounds for collections of tubes in $R^{4}$ that satisfy the polynomial Wolff axioms. In brief, a collection of $δ$ -tubes satisfies the…

Breaking the 3/2 barrier for unit distances in three dimensions

An improved bound on the Hausdorff dimension of Besicovitch sets in R3

Polynomial Wolff axioms and Kakeya-type estimates in R4

An improved bound on the Hausdorff dimension of Besicovitch sets in $R^{3}$

Polynomial Wolff axioms and Kakeya-type estimates in $R^{4}$