## Folding papers and turbulent flows

Camillo De Lellis

University of Zürich

February 23, 2017

In the fifties John Nash astonished the geometers with his celebrated isometric embedding theorems. A folkloristic explanation of his first theorem is that you should be able to put any piece of paper in your pocket without crumpling or folding it, no matter how large it is. A couple of decades later Gromov showed how Nash's ideas can be used to reinterpret other known counterintuitive facts in geometry and to discover many new ones. Ten years ago László Székelyhidi and I discovered unexpected similarities with the behavior of some classical equations in fluid dynamics.