Alex Nabutovsky
First steps in quantitative homotopy topology with applications to geometry
Abstract: Let M be a closed Riemannian manifold and f be a map of a sphere into M. If f is contractible, then how ``fast" can f be contracted to a point? Also, for each non-trivial homotopy class of maps from a sphere to M one can ask what is the minimal ``size" of a map in this homotopy class. We will provide some answers for these questions and describe their applications to geometric variational problems. At the end of the talk we will discuss some open questions.