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...
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-principle...
The field of continuous combinatorics studies large (dense)
combinatorial structures by encoding them in a "continuous" limit
object, which is amenable to tools from analysis, topology, measure
theory, etc. The syntactic/algebraic approach of "flag...
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 perspective on this...