The principal investigator will continue his study of integrable systems. In particular he will develop a new theory of webs based on an analysis of the structure equations for the G- structure associated to a web of high rank. He will also study the geometry of the moduli of Calabi-Yau three folds and the singularities of minimal Lagrangian submanifolds. 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.
