This award supports research in algebraic geometry. There are two objectives of the project. The first is to obtain universal realtions for the values of Donaldson polynomials on classes of algebraic curvs of arbitrary genus and self-intersection. The second is to understand global properties of moduli spaces of bector bundles on surfaces. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past ten years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9400835
Program Officer
Gary Cornell
Project Start
Project End
Budget Start
1994-07-01
Budget End
1995-06-30
Support Year
Fiscal Year
1994
Total Cost
$15,000
Indirect Cost
Name
University of Pennsylvania
Department
Type
DUNS #
City
Philadelphia
State
PA
Country
United States
Zip Code
19104