108 citations · 378 across the 31 of their papers we have counts for
9 papers · 1 filter
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…
The flecnode polynomial: a central object in incidence geometry
Nets Hawk Katz
We give a brief exposition of the proof of the Cayley-Salmon theorem and its recent role in incidence geometry. Even when we don't use the properties of ruled surfaces explicitly,…
Structure in additively nonsmoothing sets
Michael Bateman, Nets Hawk Katz
Sets with many additive quadruples are guaranteed to have many additive octuples, by Hölder's inequality. Sets with not many more than this are said to be additively nonsmoothing.…
On the Erdos distinct distance problem in the plane
Larry Guth, Nets Hawk Katz
In this paper, we prove that a set of points in has at least distinct distances, thus obtaining the sharp exponent in a problem of Erdös. We fol…
On Freiman's Theorem in Nilpotent Groups
David Fisher, Nets Hawk Katz, Irine Peng
We generalize a result of Tao which extends Freiman's theorem to the Heisenberg group. We extend it to simply connected nilpotent Lie groups of arbitrary step.
Algebraic Methods in Discrete Analogs of the Kakeya Problem
Larry Guth, Nets Hawk Katz
We prove the joints conjecture, showing that for any lines in , there are at most points at which 3 lines intersect non-coplanarly. We also prove…
On additive doubling and energy
Nets Hawk Katz, Paul Koester
We show that if A is a set having small subtractive doubling in an abelian group, that is |A-A|< K|A|, then there is a polynomially large subset B of A-A so that the additive energ…
A sum-product estimate in finite fields, and applications
Jean Bourgain, Nets Katz, Terence Tao
Let be a subset of a finite field for some prime . If for some , then we prove the estimate $|A+A| + |A.A| \geq c(δ) |A|^{1+\eps…
A new bound on partial sum-sets and difference-sets, and applications to the Kakeya conjecture
Nets Hawk Katz, Terence Tao
Let , be finite subsets of an abelian group, and let be such that $# A, # B, # \{a+b: (a,b) \in G \} \leq N$. We consider the question of estimating th…