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...
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 : 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: 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: 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: 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: 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: 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: 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...
