Riemannian Geometry

The course aims to introduce students to advanced topics in Riemannian geometry that are fundamental for current research in the field. In particular, various techniques will be developed to establish connections between the curvature and the topology of a manifold and its submanifolds.

A solid foundation in Riemannian geometry; familiarity with tools from Geometric Analysis (including distance function analysis and comparison theorems, function theory, differential forms, and variational methods); and the ability to use these tools to obtain topological information about a Riemannian manifold and its submanifolds.