Abstract: Enumerative algebraic geometry has enjoyed a long and
rich history since the mid 19th century. The latest chapter has been perhaps
the most exciting, and certainly the most unexpected. In 1991, string theories
began to give predictions of numbers of algebraic curves in a range of
geometric situations. Furthermore, the physics heuristics directly led
to the development of better mathematical techniques for answering the
questions of interest. This history will be reviewed, leading up to recent
progress and a look to the future. Special attention will be given to the
conjectural role of a Virasoro algebra of differential operators which
would provide relations between the gravitational correlators of an algebraic
variety, including the Gromov-Witten invariants.
alexsuciu@neu.edu