Geometric Analysis, Applications in the Analysis of Some Applied Math PDE's, and Developing Geometry Courses for Freshmen and Math Education Majors

9704488 Han The project lies in the general area of Riemannian geometry. The investigator is to pursue questions related to scalar and Gauss curvatures, geometric PDEs (vortex sheet equation), and the geometry of harmonic maps into negatively curved surfaces. The project also contains an education component involving the undergraduate geometry curriculum. Geometric partial differential equations use techniques from various areas in geometric analysis such as harmonic maps and Riemannian geometry to solve differential equations arising in a variety of contexts. For example, the vortex sheet equation is related to the evolution of vortices in the air and other fluids as well as to phase transitions in super-conductivity.