Oliver Roche-Newton

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20242026

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math.CO2026

Point sets determining few angles are almost contained in a line or circle

Krishnendu Bhowmick, Oliver Roche-Newton, Audie Warren

We prove a structural theorem for point sets in $R^{2}$ which determine few pinned angles. More precisely, we prove the existence of an absolute constant $c > 0$ such that if $…

math.CO2026

A general-position problem for planar line arrangements

Oliver Roche-Newton

For all $δ > 0$ and infinitely many $n \in N$ , we show that there exists a set $L$ of $n$ lines in $R^{2}$ such that there are no intersecting quadruples, but for every…

math.CO2025

Additive structure in convex sets

Thomas F. Bloom, Jakob Führer, Oliver Roche-Newton

This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $Ω (∣ A ∣^{3/2})$ t…

math.CO2024

A lower bound for the number of pinned angles determined by a Cartesian product set

Oliver Roche-Newton

We prove that, for any $B \subset R$ , the Cartesian product set $B \times B$ determines $Ω (∣ B ∣^{2 + c})$ distinct angles.