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 the
field...
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 flavours...
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 of a...
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 cobordisms...
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 described in...
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 applications...
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 fields, for...
