Moduli spaces of open strings have polylogarithmic Mirzakhani volumes

Abstract

We show that the Mirzakhani volume, as introduced by Chekhov, of the moduli space of every crowned hyperbolic surface is naturally expressible as a sum of Gaussian rational multiples of polylogarithms evaluated at $\pm 1$ and $\pm \sqrt{-1}$.

arXiv comment35 pages, 3 figures. Conjecture 1.7 is now Theorem 1.7