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Award Abstract #0502241
International Research Fellowship Program: Calibrated Geometries and Integrable Systems
| NSF Org: |
OISE
Office of International Science and Engineering
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| Initial Amendment Date: |
June 3, 2005 |
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| Latest Amendment Date: |
June 3, 2005 |
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| Award Number: |
0502241 |
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| Award Instrument: |
Fellowship |
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| Program Manager: |
Susan Parris
OISE Office of International Science and Engineering
O/D OFFICE OF THE DIRECTOR
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| Start Date: |
September 1, 2006 |
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| Expires: |
August 31, 2009 (Estimated) |
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| Awarded Amount to Date: |
$133870 |
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| Investigator(s): |
Daniel Fox dosmanos@math.duke.edu (Principal Investigator)
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| Sponsor: |
Fox Daniel
Durham, NC 27708 / -
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| NSF Program(s): |
EAPSI
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| Field Application(s): |
0000099 Other Applications NEC
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| Program Reference Code(s): |
OTHR, 5980, 5956, 5946, 0000
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| Program Element Code(s): |
7316
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ABSTRACT
0502241
Fox
The International Research Fellowship Program enables U.S. scientists and engineers to conduct three to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.
This award will support a twenty-two-month research fellowship by Dr. Daniel Fox to work with Dr. Dominic Joyce at Oxford University in the United Kingdom.
The goal of this project is to clarify and cultivate the connection between integrable systems and calibrated geometries. The benefit of this is two-fold. On the one hand techniques from integrable systems will lead to new methods for constructing and understanding calibrated submanifolds. On the other hand, calibrated geometry offers an ideal setting in which to develop our understanding of integrability. The primary approach will be to study the conservation laws of calibrated geometries. These techniques could lead to a characterization of calibrated geometries in terms of their conservation laws, to a better understanding of singular solutions, to new methods for constructing explicit solutions, and to a better understanding of the role of conservation laws in integrable systems. The PIs will also explore the connections between the U/K-integrable systems and the calibrated isometric embedding problems. This may lead to an intrinsic geometric description of calibrated submanifolds.
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