Séminaire de Cryptographie

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Yaacov Kopeliovich

Theta identities and Thomae formulas

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.

We present a programming challenge to fully solve the g=4 problem.