2 papers
math.CO2026
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…
math.CA2025
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…