Workshop on the h-principle and beyond

In this talk we will show how to construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space of divergence-free vector fields, for...

We introduce Lefschetz fibration structures on the Milnor fibers of simple-elliptic and cusp singularities in complex three variables, whose regular fibers are diffeomorphic to the 2-torus. We know two ways to construct them and explain h-principle...

Convex integration and the holonomic approximation theorem are two well-known pillars of flexibility in differential topology and geometry. They each seem to have their own flavor and scope. The goal of this talk is to bring new perspective on this...

Beltrami fields, that is vector fields on $\mathbb R^3$ whose curl is proportional to the field, play an important role in fluid mechanics and magnetohydrodynamics (where they are known as force-free fields). In this lecture I will review recent...

 I will discuss a remarkable generalization of Mather’s theorem by Thurston that relates the identity component of diffeomorphism groups to the classifying space of Haefliger structures. The homotopy type of this classifying space played a...

We discuss the problem of extending local deformations of solutions to open partial differential relations to global deformations and formulate conditions under which such extensions are possible. Among others these results are applied to study...

We prove the equivalence of Eliashberg overtwisted $h$—principle and  the Eliashberg-Mishachev classification of contact structures in the tight $3$-ball. I.e. we prove that simple algebraic topology computations takes us from one result to the...

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [6, 7, 8] launched a programme to address the global existence problem for the Euler and Navier-Stokes equations...