Convex Integration and Nonlinear Partial Differential Equations

Significant advances in the field of convex integration will be explained and discussed by world leading specialists involved in the subject's resurgence. Convex integration originated with the Nash-Kuiper (1954/55) isometric embedding theorem and is central to Gromov's h-principle (1986). The highly irregular (wrinkled) solutions which are a prominent feature have recently found application to other important contexts. Long standing conjectures such as that by Onsager on turbulence have been successfully resolved. Connexions have been established with several nonlinear partial differential equations including those for fluid and solid continuum mechanics. Numerical simulation of solutions has enhanced intuition and illustrated geometrical and physical properties. Challenging open problems however, remain and offer a rich potential for future research. These topics form the main themes of the workshop.

Professor Camillo De Lellis (IAS) will deliver the Clay Lecture at the workshop. (video of November 8 lecture) (video of November 9 lecture)