4 papers
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…
Valuative independence and cluster theta reciprocity
Man-Wai Cheung, Timothy Magee, Travis Mandel +1
We prove that theta functions constructed from positive scattering diagrams satisfy valuative independence. That is, for certain valuations , we have $\oper…
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…
A short proof of the finiteness of Dynkin friezes
Greg Muller
We give a short and elementary proof that every Dynkin diagram admits finitely many (positive integral) friezes. This was originally proven by Gunawan-Muller using the geometry of…