# Special year - math workshop

Nov
01
2021

### Workshop on the h-principle and beyond

9:00am

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...

Nov
01
2021

### Workshop on the h-principle and beyond

Looking at Euler flows through a contact mirror: Universality, Turing completeness and undecidability
Eva Miranda
9:00am|Simonyi Hall 101 and Remote Access

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...

Nov
01
2021

### Workshop on the h-principle and beyond

Overtwisted = Tight in 3 dimensions
Francisco Presas Mata
10:15am|Simonyi Hall 101 and Remote Access

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...

Nov
01
2021

### Workshop on the h-principle and beyond

Local flexibility for open partial differential relations
Bernhard Hanke
11:45am|Simonyi 101 and Remote Access

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...

Nov
01
2021

### Workshop on the h-principle and beyond

Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups
Sam Nariman
2:15pm|Simonyi 101 and Remote Access

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...

Nov
02
2021

### Workshop on the h-principle and beyond

The many facets of complexity of Beltrami fields in Euclidean space
Daniel Peralta-Salas
9:00am

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...

Nov
02
2021

### Workshop on the h-principle and beyond

Holonomic Approximation through Convex Integration
Mélanie Theilliere
10:15am|Simonyi 101 and Remote Access

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...

Nov
02
2021

### Workshop on the h-principle and beyond

Lefschetz fibrations on the Milnor fibers of cusp singularities and applications
Yoshihiko Mitsumatsu
11:45am|Simonyi 101 and Remote Access

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...

Nov
02
2021

### Workshop on the h-principle and beyond

Chaos in the incompressible Euler equation on manifolds of high dimension
Francisco Torres de Lizaur
2:15pm|Simonyi 101 and Remote Access

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...

Nov
03
2021

### Workshop on the h-principle and beyond

The flexibility of caustics and its applications
Daniel Alvarez-Gavela
11:45am|Simonyi 101 and Remote Access

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...