# Special Year 2021-22: Workshop on the h-principle and Beyond

### Workshop on the h-principle and beyond

November 02, 2021 | 2:15pm - 3:15pm

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...

### Workshop on the h-principle and beyond

November 02, 2021 | 11:45am - 12:45pm

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...

### Workshop on the h-principle and beyond

November 02, 2021 | 10:15am - 11:15am

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...

### Workshop on the h-principle and beyond

November 02, 2021 | 9:00am - 10:00am

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...

### Workshop on the h-principle and beyond

November 01, 2021 | 2:15pm - 3:15pm

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...

### Workshop on the h-principle and beyond

November 01, 2021 | 11:45am - 12:45pm

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...

### Workshop on the h-principle and beyond

November 01, 2021 | 10:15am - 11:15am

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...

### Workshop on the h-principle and beyond

November 01, 2021 | 9:00am - 10:00am

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...

### Workshop on the h-principle and beyond

November 01, 2021 | 9:00am - November 05, 2021 | 5:00pm

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

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

### Clay Research Conference - an Online Event

September 30, 2021 | 5:10pm - 5:45pm

**Limited seating is available in Simonyi Lecture Hall and is by invitation only for IAS members or faculty. Remote access will be given to those that register.  Please contact Naomi Kraker at admin@claymath.org to receive the zoom link for the...