From Nash to Onsager, I

In this series of lectures we will:
- give a complete proof of Nash's theorem on the existence of C1 isometric embeddings in codimension 2
- discuss briefly Kuiper's improvement and how to modify Nash's approach to achieve C1;embeddings
- give a complete proof of the existence of bounded nontrivial compactly supported solutions of the Euler equations, using the Baire Category method and the Lipschitz convex integration method
- draw a parallel between the two problems, motivating the second part of the course given by Laszlo Szekelyhidi Jr.