1 citations · 1 across the 5 of their papers we have counts for
8 papers
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…
Ergodic theoretic proof of equidistribution of Hecke points
Alex Eskin, Hee Oh
We use the theory of unipotent flows to prove, in a general setting, the equidistribution of Hecke points. We follow the approach of Burger-Sarnak, and use a theorem of Mozes-Shah.
Representations of integers by an invariant polynomial and unipotent flows
Alex Eskin, Hee Oh
We study a refined version of the Linnik problem on the asymptotic behavior of the number of representations of integer by an integral polynomial as tends to infinity. We a…
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…
The theta characteristic of a branched covering
Alex Eskin, Andrei Okounkov, Rahul Pandharipande
We give a group-theoretic description of the parity of a pull-back of a theta characteristic under a branched covering. It involves lifting monodromy of the covering to the semidir…
Moduli Spaces of Abelian Differentials: The Principal Boundary, Counting Problems and the Siegel--Veech Constants
Alex Eskin, Howard Masur, Anton Zorich
A holomorphic 1-form on a compact Riemann surface S naturally defines a flat metric on S with cone-type singularities. We present the following surprising phenomenon: having found…