Title: From a Question of S.-S. Chern to the Geometry of Strongly Minimal Submanifolds: New Inequalities for Curvature

Abstract: In 1968, S.-S. Chern raised to attention the question that there might be further Riemannian obstructions for a manifold to admit an isometric minimal immersion into an Euclidean space. This question triggered a whole new direction of study in the geometry of submanifolds. ?In the last two decades, there have been important advances in the study of new curvature invariants, many of these efforts due to B.-Y. Chen. We will present a few recent developments in this theory, and we focus our attention on several classes of inequalities in the geometry of submanifolds in Riemannian and Kaehlerian context.