Description
In this talk we apply Thomae formulas to obtain algebraic relations satisfied by Riemann surfaces that are cyclic covers of the Sphere. We focus on the genus 2 case and then give an example of a higher genus case (g=4) that was not known before. The conjectural connection of these identities as well as Thomae formulas to the moduli action of the Braid group is explained.<br/> We present a programming challenge to fully solve the g=4 problem.