Statistics of Square-tiled Surfaces: Symmetry and Short Loops
arXiv:1902.08214
Abstract
Square-tiled surfaces are a class of translation surfaces that are of particular interest in geometry and dynamics because, as covers of the square torus, they share some of its simplicity and structure. In this paper, we study counting problems that result from focusing on properties of the square torus one by one. After drawing insights from experimental evidence, we consider the implications between these properties and their frequency in each stratum of translation surfaces.
arXiv comment18 pages
References in corpus (6)
- Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
- An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum
- Orbitwise countings in H(2) and quasimodular forms
- Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata
- Equidistribution of saddle connections on translation surfaces
- The probability of generating the symmetric group with a commutator condition