Singular moduli on Shimura curves

我的工作是研究下村曲线，它是某些曲面的参数空间，称为QM阿贝尔曲面。下村曲线理论应该类似于模曲线理论，因为两者是非常相关的。模曲线理论在费马大定理和许多其他重要的数学问题的求解中起到了非常重要的作用。我的工作是将已有的结果从模曲线推广到Shimura曲线，我的结果具有很强的计算量，因此具有广泛的应用。

My work is on studying Shimura curves, which are parameter spaces of certain surfaces called QM abelian surfaces. The theory of Shimura curves is expected to resemble the theory of Modular curves as the two are very connected. The theory of Modular curves has been very instrumental in the solution of Fermat's Last Theorem, and many other important mathematical problems. My work is based on extending known results from Modular curves to Shimura curves, my results are very computational and thus have wide application.