3 papers
math.DS2026
Affine mappings of translation surfaces: shrinking targets and Diophantine properties
Chris Judge, Josh Southerland
Let be a translation surface whose Veech group is a lattice. We prove that the generic orbit of the group of affine homeomorphisms of can be used to approximate…
math.GT2024
Cylinder decompositions on geometric armadillo tails
Dami Lee, Josh Southerland
We study a class of finite-area, infinite-type translation surfaces, and find an explicit cylinder decomposition on these surfaces which do not manifest on finite-type translation…
math.DS2024
An Effective Slope Gap Distribution for Lattice Surfaces
Tariq Osman, Joshua Southerland, Jane Wang
We prove an effective slope gap distribution result first for the square torus and then for general lattice translation surfaces. As a corollary, we obtain a dynamical proof for an…