Groups Actions and Rigidity in Riemannian Geometry.
Riemannian manifolds are an abstraction of spaces possessing a notion of distance.
These are abstract spaces in that a Riemannian manifold does not have to sit inside an ambient space, unlike curves and surfaces in 3-space. The overall shape of such a space is then determined by its so called topology as well as the distance function. The proposed research has to do with understanding this interaction between the topology and distance function. More on THIS Work .