This conference is devoted to asymptotic and effective results in complex geometry. Many important problems in complex and algebraic geometry concern the construction of holomorphic objects such as holomorphic sections of line bundles or maps between spaces. It often happens that the construction problem simplifies as the degree of the line bundles or maps increases. A classical example is the Kodaira embedding theorem, which says that there are enough sections of a high power of a positive line bundle to embed a Kahler manifold into projective space. Asymptotic results in general concern the properties of maps or sections of very high degree, where constructions often simplify. Effective results ask for the smallest power or degree where a desired effect takes place, e.g. the smallest power of a line bundle so that sections embed. Many such results will be surveyed in our conference, with techniques ranging from partial differential equations to geometric and algebraic methods.

Our conference consists of seven days of lectures, with six to eight lectures a day. There will be lectures surveying past results and others which present new results. The topics include complexity of zero-finding algorithms, moduli spaces, holomorphic maps, ground states of superconductors, and the vacuum selection problem in string theory. The lectures will expose the field to graduate students, postdoctoral researchers and junior faculty members, as well as to senior mathematicians. Two graduate students and at least five postdocs are giving lectures. A significant portion of our funding will go towards paying travel expenses of graduate students, young mathematicians and members of under-represented groups.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
0326849
Program Officer
Joe W. Jenkins
Project Start
Project End
Budget Start
2004-05-01
Budget End
2005-04-30
Support Year
Fiscal Year
2003
Total Cost
$21,000
Indirect Cost
Name
Johns Hopkins University
Department
Type
DUNS #
City
Baltimore
State
MD
Country
United States
Zip Code
21218