Schottky Groups and the construction of higher genus Frobenius manifolds

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The moduli space of holomorphic maps from a Riemann surface to the sphere can be equipped with the structure of a Frobenius Manifold. For genus zero (where the maps are rational) and genus one (where the maps are elliptic functions) this structure has been constructed explicitly. For higher genus, existence results are known, but no explicit solutions have been constructed. The project aims to rectify this by using the Schottky-Klein prime function to construct the holomorphic maps explicitly, drawing on recent work of Strachan (genus 1 solutions) and also work of Crowdy who has used the Schottky-Klein prime function to solve higher-genus potential theory problems.