Frobenius manifolds from a geometrical and categorical viewpoint

本项目旨在提供从代数曲线中以不同方式得到的Frobenius流形之间的联系。不同的构造，一方面使用复杂几何，另一方面使用范畴论，分别提供了对同一个Frobenius流形的定量和定性观点。总之，这些不同的观点允许计算以前无法获得的物理量，并指出代数几何、复杂几何和微分几何之间深刻的新关系。这些关系有望在数学和物理的边界上指导新的基础研究。

This project aims to provide connections between Frobenius manifolds obtained from algebraic curves in diverse ways. The different constructions, using complex geometry on the one hand and category theory on the other, provide, respectively, a quantitative and qualitative view on the same Frobenius manifold. Together, these distinct points of view allow for the calculation of previously inaccessible physical quantities, and point to deep new relations between algebraic, complex and differential geometry. These relations are expected to guide new fundamental research on the border of mathematics and physics.