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.
