Departmental Colloquium
Sheldon Katz
University of Illinois at Urbana-Champaign
Enumerative Geometry via String Theory
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.
Friday October 21, 2005 at 3:00 PM in SEO 636