Adam Sheffer

activity

20242026

collaborators

4 papers

math.CO2026

The Minimum Number of Plane Graphs for Sets with Small Hulls

Alice Chen, Tara Saini, Adam Sheffer +1

Let $P$ be a set of $n$ points in $R^{2}$ , with a convex hull of size $O (n / lo g n)$ . We prove that $I^c ◯ (12.2 4^{n})$ plane graphs can be drawn on $P$ , the fi…

math.NT2026

A combinatorial large sieve for Sidon sets, distances, and norm forms

Ernie Croot, Junzhe Mao, Cosmin Pohoata +2

We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence…

math.MG2025

Distinct Distances on Pfaffian Curves

Abhiram Natarajan, Adam Sheffer

We generalize Pach and de Zeeuw's bound for distinct distances between points on two curves, from algebraic curves to Pfaffian curves. Pfaffian curves include those that can be def…

math.CO2024

Expected degrees in random plane graphs

Neely Lovvorn, Oscar Murillo-Espinoza, Adam Sheffer

We prove that, for every set of $n$ points $P$ in $R^{2}$ , a random plane graph drawn on $P$ is expected to contain less than $n /10.18$ isolated vertices…