Members’ Seminar

In a series of works with Laszlo Szekelyhidi Jr. we pointed out an unusual analogy between two problems in rather distant areas: a long standing conjecture of Onsager in the theory of turbulence and a (less known) critical regularity problem in classical differential geometry. In both cases the issue is to find the critical regularity above which the solutions to a certain system of partial differential equations are well-behaved'' and below which they are instead rather wild''. The circle of ideas which, thanks to the contributions of several people, have solved both problems leads also to other surprising facts and raises many further questions.