Sheldon Katz : Enumerative Geometry via String Theory

Posted by , part of the Departmental Colloquium.

At

Oct. 21, 2005, 3 p.m.

In

SEO 636

Abstract

The goal of enumerative geometry is to count geometric configurations satisfying prescribed geometric conditions. A classical example: there are exactly 2 lines in space meeting each of 4 lines in general position. But many other 19th century problems remained unsolved for more than a century. During the last 15 years, enumerative geometry has been revitalized from an unlikely source: string theory in physics. The ideas of string theory gave birth to entirely new areas of geometry which have been used to solve classical enumerative questions (and much more). In this talk I give some perspective on enumerative geometry and explain how string theory has given new insight about the enumeration of curves. I also illustrate with examples and give some prospects for the future.