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math.DS2005
Pillowcases and quasimodular forms
Alex Eskin, Andrei Okounkov
We prove that natural generating functions for enumeration of branched coverings of the pillowcase orbifold are level 2 quasimodular forms. This gives a way to compute the volumes…
math.DS2004
Unipotent flows on the space of branched covers of Veech surfaces
Alex Eskin, Jens Marklof, Dave Witte Morris
There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup $U = {\begin{pmatrix} 1 & * 0 & 1 \end{pmatrix…