Seminar Analysis: Antoine Choffrut (University of Edinburgh)

Geometry in the Euler equations of hydrodynamics: h-principle and convex integration

The following dichotomy between rigidity and flexibility is now well known in geometry: while uniqueness holds for smooth solutions to the isometric embedding problem, the set of solutions becomes unimaginably large if one allows rough ones. What is surprising is that this dichotomy holds for problems coming from mathematical physics,and in particular the Euler equations of fluid dynamics. In this (mainly expository) talk I will explain the h-principle and the method of convex integration. Convex geometry is the heart of the matter and profuse figures will attempt to illustrate the difficulties and how to tame them.

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