Simon 9504456 Two related topics of research are proposed: singularities of energy minimizing maps and curvature flows. Simon pioneered analytic techniques for studying the top-dimensional singular set of an energy minimizing map, for which he recently won the Bocher prize. In addition to continuing this research - which could lead to a resolution of the important conjecture asserting that minimizers of energy are stratified manifolds - several problems on curvature flows are proposed. Proposed curvature flow problems model a wide range of phenomena, such as the dynamics of soap films, immiscible fluids and crystal growth, and lie in the area of nonlinear parabolic partial differential equations.
