Award: DMS 1105832, Principal Investigator: Dmitry Tamarkin

These research projects concentrate on issues related to the microlocal approach to categories associated with symplectic manifolds, such as the Fukaya category. It is anticipated that by applying algebraic tools such as differential graded categories and higher categories, will yield geometric simplifications by avoiding transversality and other geometric conditions that can be hard to provide.

Symplectic geometry is the study of the background structure for the Hamiltonian version of classical mechanics. The study of this kind of geometry was revolutionized in the 1980s by the use of analytic techniques involving maps of surfaces into symplectic manifolds, a point of view that led more recently to the Fukaya categories invoked below. These Fukaya categories carry a lot of significant information about the underlying symplectic manifold, and it would be useful to have a less subtle description of them than the original definition.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1105832
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
2011-10-01
Budget End
2014-09-30
Support Year
Fiscal Year
2011
Total Cost
$136,032
Indirect Cost
Name
Northwestern University at Chicago
Department
Type
DUNS #
City
Evanston
State
IL
Country
United States
Zip Code
60201