3 papers
math.AG2026
Point Counts of Cluster Varieties of Marked Surfaces Over Finite Fields
James Beyer
We establish formulae for point counts of cluster varieties of cluster algebras of marked surfaces, possibly with punctures. We then establish formulae for the number of non-deep p…
math.CO2025
Separating dots with circles
James Beyer, Jaewon Min, Greg Muller
Given a finite set of points in general position in the plane or sphere, we count the number of ways to separate those points using two types of circles: circles through three of t…
math.AG2024
Deep Points of Cluster Algebras
James Beyer, Greg Muller
We initiate a systematic study of the deep points of a cluster algebra; that is, the points in the associated variety which are not in any cluster torus. We describe the deep point…