5 citations · 15 across the 9 of their papers we have counts for
9 papers
Densities of arithmetic Hecke triangle group orbits
Samantha Fairchild, Christopher R. H. Hanusa
We give new proofs computing the asymptotic densities for orbits of the arithmetic Hecke triangle groups when and . We use elementary number theory techniques alon…
Average degree of the essential variety
Paul Breiding, Samantha Fairchild, Pierpaola Santarsiero +1
The essential variety is an algebraic subvariety of dimension in real projective space which encodes the relative pose of two calibrated pinhole camera…
Pairs in discrete lattice orbits with applications to Veech surfaces
Claire Burrin, Samantha Fairchild, Jon Chaika
Let , be two discrete orbits under the linear action of a lattice on the Euclidean plane. We prove a SiegelVeech-type integral formula f…
Crossing the transcendental divide: from translation surfaces to algebraic curves
Türkü Özlüm Çelik, Samantha Fairchild, Yelena Mandelshtam
We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified…
Shrinking rates of horizontal gaps for generic translation surfaces
Jon Chaika, Samantha Fairchild
A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many sing…
Counting pairs of saddle connections
J. S. Athreya, S. Fairchild, H. Masur
We show that for almost every translation surface the number of pairs of saddle connections with bounded magnitude of the cross product has asymptotic growth like where the…
Families of well approximable measures
Samantha Fairchild, Max Goering, Christian Weiß
We provide an algorithm to approximate a finitely supported discrete measure by a measure corresponding to a set of points so that the total variation between a…
A higher moment formula for the Siegel--Veech transform over quotients by Hecke triangle groups
Samantha K. Fairchild
We compute higher moments of the Siegel--Veech transform over quotients of by the Hecke triangle groups. After fixing a normalization of the Haar measure on $SL(…
The Abelian Sandpile Model on Fractal Graphs
Samantha Fairchild, Ilse Haim, Rafael G. Setra +2
We study the Abelian sandpile model (ASM), a process where grains of sand are placed on a graph's vertices. When the number of grains on a vertex is at least its degree, one grain…