A team of four geometers will investigate a variety of problems in complex differential geometry, Riemannian geometry, and related areas. The role of spaces of algebraic cycles in universal constructions in topology and homology-cohomology theory will be carefully studied. Work will progress on establishing the existence of Kahler-Einstein metrics on open manifolds, on the structure of p-Kahler spaces in Moishezon geometry, and on the structure of Riemannian 4-manifolds with boundary. The team of investigators will establish more of the ground work necessary for the understanding by physicists of our four dimensional space-time. The connections between the branch of mathematics broadly referred to as "differential geometry," and cosmological physics dates back to Einstein; the mathematical theory which Einstein applied goes back even further to Gauss and Riemann in the nineteenth century. The group being funded here maintains close connections with physicists, and steers their research in directions of current excitement both to mathematicians and physicists.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8901303
Program Officer
James Glazebrook
Project Start
Project End
Budget Start
1989-06-01
Budget End
1993-05-31
Support Year
Fiscal Year
1989
Total Cost
$439,556
Indirect Cost
Name
State University New York Stony Brook
Department
Type
DUNS #
City
Stony Brook
State
NY
Country
United States
Zip Code
11794