Seminars Sorted by Series

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...

ABSTRACT: We describe a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be...

Abstract: The "c-principle" is a cousin of Gromov's h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that  for the MT-theorem, when the base dimensions is not equal four, only the mildest...

Abstract: Let f be an embedding of a non compact manifold into an Euclidean space and p_n be a divergent sequence of points of M. If the image points f(p_n) converge, the limit is called a limit point of f. In this talk, we will build an embedding f...

Abstract: In this talk we consider the classical Monge-Amp´ere equation in two dimensions in a low-regularity regime:

(0.1) det D 2u = f on D ⊂ R2 .

We will assume that f is a given strictly positive, smooth function, but we want to assume as...

Abstract: In the first half of the talk I will review Gromov's work on convex integration for open differential relations. I will put particular emphasis on comparing various flavours of ampleness and, in particular, I will note that the different...

Abstract: Traditionally, objects of study in symplectic geometry are smooth - such as symplectic and Hamiltonian diffeomorphisms, Lagrangian (or more generally, isotropic and co-isotropic) submanifolds etc. However, in the course of development of...

Abstract : We describe a construction of a locally conformal symplectic structure homotopic to any given non-degenerate 2-form and whose Lee form can be any non-exact 1-form. Moreover, each connected component of the boundary, if any, may be chosen...

Abstract: Cieliebak and Eliashberg showed that there is a special class of flexible symplectic structures that satisfy an h-principle and hence  have `trivial' symplectic topology. In this talk, I will explain that it is fruitful to think of...

Abstract: I use the same title for different talks, changing the selection of topics and the level of detailedness for each topic:) This is a survey talk based on joint projects with D. Chen, S. Ivanov, late Ya. Kurylev, M. Lassas, J. Lu, and, if...