Sharp Szemer\'edi-Trotter Constructions in the Plane
Larry Guth, Olivine Silier

TL;DR
This paper introduces a novel family of sharp point-line incidence examples in the plane, breaking from traditional lattice-based constructions, and applies these findings to the inverse Loomis-Whitney problem.
Contribution
It provides the first non-lattice-based sharp examples for the Szemerédi-Trotter theorem and connects these to the inverse Loomis-Whitney problem.
Findings
New non-lattice sharp examples for Szemerédi-Trotter theorem
Application to discrete inverse Loomis-Whitney problem
Advancement in understanding point-line incidences
Abstract
We present a new family of sharp examples for the Szemer\'edi-Trotter theorem. These are the first examples not based on a rectangular lattice. We also include an application to the discrete inverse Loomis-Whitney problem.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Combinatorial Mathematics
