Functoriality of Gromov--Witten theory

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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.