4 papers
Noncongruence cusp forms, Veech groups and enumeration
John Rached
We prove the existence of weight 2 modular forms for some Veech groups, whose Fourier coefficients at a cusp determine the counts of numbers of branched Galois covers of punctured…
The boundary of a totally geodesic subvariety of moduli space
Frederik Benirschke, Benjamin Dozier, John Rached
We consider subvarieties of , the moduli space of genus Riemann surfaces with marked points, that are totally geodesic with respect to the Teichmülle…
Separation of horocycle orbits on moduli space in genus 2
John Rached
We prove a quantitative closing lemma for the horocycle flow induced by the -action on the moduli space of Abelian differentials with a double-order zero…
Counting Closed Geodesics in Rank 1 -orbit Closures
John Rached
We obtain bounds on the numbers of intersections between triangulations as the conformal structure of a surface varies along a Teichm{ü}ller geodesic contained in an $\mathrm{SL}\l…