Computational Methods for Schottky Uniformization and the Java Oorange Environment

The numerical treatment of Riemann surfaces of higher genus is a challenging problem. We developed methods based on Schottky uniformization which we used in many applications involving examples up to genus 12. The talk gives a short introduction to Schottky uniformization and those closely related Poincaree Theta series which express differentials and integrals. We will briefly discuss numerical issues of the evaluation of these series and will present the results of our evaluation algorithms. Finally, we give a software demonstration and develop from scratch a non-trivial application utilizing our methods in the Java Oorange Environment.