Significant advances in the field of convex integration were explained and discussed by 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 in 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 remain, however and offer a rich potential for future research. These topics formed the main themes of the Workshop.

 

The workshop, which included an expository course by Clay lecturer De Lellis, to supplement the research presentations, was open to all and especially those from the UK and international communities who wished to either acquire or expand knowledge of this intriguing theory and its striking applications.