Enumerative geometry and quantum field theory


Sheldon Katz

(Oklahoma State University)



Room 2-190

4:30 p.m., Thursday, February 26, 1998

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.

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