Mario Micallef will continue his work in the following three areas: Riemannian manifolds with non-negative curvature on isotropic two-planes; minimal surfaces in flat tori; harmonic maps between complete, negatively curved manifolds. The notion of curvature on isotropic two-planes was introduced recently in joint work of Micallef and Moore. Positivity of this curvature seems to be the correct generalization of such classical notions as pinching of the sectional curvature and positive curvature operator. Micallef will proceed furhter towards a classification of compact manifolds which admit metrics of positive curvature on isotropic two-planes. The study of minimal surfaces in flat tori will hopefully yield the first examples of stable minimal surfaces in manifolds of non-negative sectional curvature which are not holomorphic with respect to any Kahler structure on the ambient manifold.
