Schottky Groups and the construction of higher genus Frobenius manifolds

从黎曼曲面到球面的全纯映射的模空间可以具有Frobenius流形的结构。对于亏格零（其中映射是有理的）和亏格一（其中映射是椭圆函数），这个结构已经被明确地构造出来。对于更高的亏格，存在性结果是已知的，但没有显式的解决方案已经构造。该项目的目的是纠正这一点，使用的肖特基-克莱因素函数来构建全纯映射明确，借鉴最近的工作斯特拉坎（属1的解决方案），也工作的克劳迪谁使用的肖特基-克莱因素函数，以解决更高的属潜在的理论问题。

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.