Principal Investigator: Yongbin Ruan
During the past twenty years, there has been a great deal of interaction between mathematics and physics. An important area of this interaction involves the theory of Gromov-Witten invariants. In physics, it counts the instantons corrections of Calabi-Yau space. In mathematics, it provides important invariants for algebraic and symplectic geometry. Inspired by both mathematics and physics, Gromov-Witten theory has been established in a variety of situations such as relative Gromov-Witten theory and orbifold Gromov-Witten theory. Each of them is an integral part of the big picture and they have been essential for a complete understanding of Gromov-Witten theory. This proposal seeks to advance Gromov-Witten theory in two directions; (i) expanding Gromov-Witten theory to the Landau-Ginzburg/singularities model and developing it as an effective computational tool for ordinary Gromov-Witten theory; (ii) applying Gromov-Witten theory to study symplectic birational geometry.
Mathematics is always an important tool and language in our understanding of the structure of the universe we live in. In the string theoretic model of the universe, modern mathematical subjects such as geometry and topology play an ever bigger role. In particular, Gromov-Witten invariants enter these models as important physical quantities called instanton corrections. This project will improve our ability to calculate instanton corrections and hence enhance our understanding of the possible structure of the universe.
