The principal investigators will continue their research in the cross disciplinary area of topology and differential geometry. In particular they will study topological aspects of Monge-Ampere foliations, harmonic representatives of homotopy classes of maps between spheres, and Einstein metrics on four manifolds. The award will support travel for the principal investigators, graduate students, and visitors to Tulane University. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.
