The principal investigators will continue their work in differential geometry, hermitian geometry, and differential topology. In particular, they will study volume-minimizing cycles in Grassmann manifolds, fibrations of spheres by great spheres, stratified spaces, Einstein metrics and symplectic geometry. This award will continue support for one of the strongest programs in differential geometry in the country. In addition to their research, the principal investigators will be expected to continue making a strong contribution to education at the graduate and undergraduate level as well as their work with high school teachers and students. 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.
