Principal Investigator: Yuan-Pin Lee
The main focus of this project is to study Gromov--Witten theory and its relations and applications to other areas of mathematics, including enumerative geometry, integrable systems, K-theory, and representation theory. The emphasis is placed on some key problems where these areas intersect. These problems include the study of higher spin curves, quantum K-theory, enumerative geometry, and Frobenius manifolds.
Gromov--Witten theory was born in early 1990's through the interaction of mathematics and physics. On the mathematical side, it starts with Gromov's invention of a new way to produce symplectic invariants. On the physical side, it was Witten's study of string theory. Although of a relatively short history, Gromov--Witten theory is a major active field of research. This is due not only to its powerful solutions to old problems, but also to its interdisciplinary nature, with continuing inputs from several fields of mathematics and string theory. This project proposes to investigate Gromov--Witten theory through various perspectives and to search for its applications in other subject areas.
