37 citations · 136 across the 23 of their papers we have counts for
32 papers
Distinct Distances in Between Quadratic and Orthogonal Curves
Toby Aldape, Jingyi Liu, Gregory Pylypovych +2
We study the minimum number of distinct distances between point sets on two curves in . Assume that one curve contains points and the other points. Our main results: (…
The constant of point-line incidence constructions
Martin Balko, Adam Sheffer, Ruiwen Tang
We study a lower bound for the constant of the Szemerédi-Trotter theorem. In particular, we show that a recent infinite family of point-line configurations satisfies $I({\mathcal P…
A structural Szemerédi-Trotter Theorem for Cartesian Products
Adam Sheffer, Olivine Silier
We study configurations of points and lines that form incidences, when the point set is a Cartesian product. We prove structural properties of such configurati…
Distinct distances on non-ruled surfaces and between circles
Surya Mathialagan, Adam Sheffer
We improve the current best bound for distinct distances on non-ruled algebraic surfaces in . In particular, we show that points on such a surface span $Ω\left(n…
Distinct distances in the complex plane
Adam Sheffer, Joshua Zahl
We prove that if is a set of points in , then either the points in determine complex distances, or is contained in a line with slope $\pm…
On the Number of Discrete Chains
Eyvindur Ari Palsson, Steven Senger, Adam Sheffer
We study a generalization of Erd\H os's unit distances problem to chains of distances. Given a set of points, and a sequence of distances ,…