9503635 Wentworth This project lies in the area of smooth four-manifolds, more specifically, Donaldson theory. The investigator wants to find necessary and sufficient conditions for the existence of symplectic structures on smooth four-manifolds; to find the Donaldson series for the complex projective plane; to understand how the Donaldson series is affected under certain birational transformations. The modern study of smooth four-dimensional spaces was initiated, in large measure, by the work of Simon Donaldson in the early eighties; Donaldson used ideas from theoretical physics - Yang-Mills equations and gauge theories - in an ingenious way to help classify smooth four-manifolds. It is worth mentioning that Nathan Seiberg and Edward Witten have recently come up with an easier and more direct theory of smooth four-manifolds, again motivated by ideas from theoretical physics, namely monopoles and string theory.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9503635
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
1995-07-01
Budget End
1999-06-30
Support Year
Fiscal Year
1995
Total Cost
$60,000
Indirect Cost
Name
University of California Irvine
Department
Type
DUNS #
City
Irvine
State
CA
Country
United States
Zip Code
92697