The proposed research deals with the interaction between Gromov--Witten theory and other subjects in mathematics and physics, including birational geometry, moduli of curves, K-theory, integrable systems, and mirror symmetry. Some of the main problems investigated are: the structure of the tautological rings, quantum cohomology under birational transformations, Virasoro symmetries, and orbifold mirror symmetry.
Gromov--Witten theory lies in the intersection of many exciting research areas in mathematics and physics. On the one hand, the theory itself has some remarkable conjectural structures. Proof of these conjectures and discovery of new ones will require some new insights into the theory and input from other areas. On the other hand, it has also provided many powerful ideas and deep connections in many directions from string theory to classical subjects in mathematics. Some of these ideas and connections will be explored in this proposal.
