The principal investigator will study various aspects of Lagrangian submanifolds in symplectic geometry. This will involve an analysis of the relationship between symplectic structures and the Riemannian structure of Kahler manifolds. This investigation will include, as a model case, the study of minimal submanifolds and their mean curvature evolutions. Symplectic geometry has a long history of success as a framework in which difficult questions in mechanics can be formulated and solved. The principal investigator will use connections between this theory and complex Kahler manifolds especially as related to minimal submanifolds. Such surfaces are modeled by soap films and have been the objects of intense mathematical research in recent years.
