Speaker: Esteban Paduro

Abstract:

As everybody know you cannot isometrically embed a flat torus in R^3, or can you? The Nash embedding theorems are two theorems from the ’50 that deal with the question of isometrically embed Riemannian manifolds in R^d and will give us the answer to the previous question. One of the theorems has an easy proof but very counterintuitive conclusions and the other is very technical but the result is not that surprising.  I will present the theorems, some consequences, and sketch their proofs, both of which had a profound impact in later developments in analysis and PDE.