Manifolds with special holonomy and calibrated geometry have important relations with symplectic geometry, complex geometry, algebraic geometry, Cartan-Kahler Theory and Seiberg-Witten Theory. In this project, the P.I. plans to continue her work on calibrated submanifolds of Calabi-Yau, G_2 and Spin(7) manifolds. In joint work with S. Akbulut, the P.I. studied complex associative and complex Cayley submanifolds and using the SW theory she showed that the moduli space of these submanifolds is smooth without any obstructions to such deformations. She also introduced the mathematical definitions of mirror Calabi-Yau and G_2 manifolds. The P.I. plans to continue her work on compactification problems of these moduli spaces and to study the mirror dualities in other Calabi-Yau and G_2 manifolds. These will lead to the construction of new counting invariants and provide a better understanding of the mirror symmetry phenomenon.

The research topics of this project are motivated by questions in geometry and topology of low dimensional manifolds and mathematical physics. The P.I. believes that this makes calibrated geometry an excellent subject for students who might decide to study math and science, and as a female researcher in this exciting area she feels a particular responsibility to encourage young women to begin and to continue their studies of mathematics. She will continue to encourage both undergraduate and graduate students and to collaborate with them in this research field which is expected to have a long-lasting impact on both mathematics and physics.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1105663
Program Officer
Joanna Kania-Bartoszynska
Project Start
Project End
Budget Start
2011-08-15
Budget End
2014-07-31
Support Year
Fiscal Year
2011
Total Cost
$126,745
Indirect Cost
Name
University of Rochester
Department
Type
DUNS #
City
Rochester
State
NY
Country
United States
Zip Code
14627