Functoriality of Gromov--Witten theory

所提出的研究是关于Gromov-Witten理论与数学和物理中的其他学科之间的相互作用，包括二次几何、曲线的模数和镜面对称性。该提议的主题是格罗莫夫-威腾理论在Crepant变换下的功能性质和奥比霍尔德范畴中的镜像对称性。格罗莫夫-威滕理论位于数学和物理中许多令人兴奋的研究领域的交集。一方面，该理论本身具有惊人的猜想结构。研究这些结构需要对理论有一些新的见解，并需要来自其他领域的投入。这为数学经典学科提供了许多有趣的问题。另一方面，它也有助于发现现有数学之间的深层联系和联系。

The proposed research lies on the interaction between Gromov--Witten theory and other subjects in mathematics and physics, including birational geometry, moduli of curves, and mirror symmetry. The main themes of the proposal are the functoriality of Gromov--Witten theory under crepant transformations and the mirror symmetry in the orbifold category.Gromov--Witten theory lies in the intersection of many exciting research areas in mathematics and physics. On the one hand, the theory itself has remarkable conjectural structures. Investigating these structures requires some new insights into the theory and input from other areas. This provides a lot of interesting problems for classical subjects in mathematics. On the other hand, it also helps to discover deep relations and connections between existing mathematics.