Special year - math workshop

Organizers: Kai Cieliebak, Camillo De Lellis, Yakov Eliashberg, Emmy Murphy, László Székelyhidi Jr.

The aim of the workshop is to bring together researchers working in different areas of geometry, dynamical systems, and PDEs which have been and...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract: 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...

Abstract:  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...

Abstract: 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...

Abstract: Singularities of smooth maps are flexible: there holds an h-principle for their simplification. I will discuss an analogous h-principle for caustics, i.e. the singularities of Lagrangian and Legendrian wavefronts. I will also discuss...