Gromov-Witten theory: From curve counts to string theory

摘要

Enumerative gemoetry is a discipline with roots dating back to antiquity, but it experienced an unexpected revolution in the late twentieth century when theoretical physicists became interested in its connection to string theory. The structure of physical systems led to striking predictions about curve-counting, and the field of Gromov-Witten theory grew up around mathematicians' attempts to explain rigorously why such predictions should hold. This chapter is a broad overview of the subject of Gromov-Witten theory, giving a tour of some of the fundamental definitions, methods, and open questions in the field.