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...
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 recent...
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...
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
study...
We give a new proof of the fact that the parallel repetition of
the (3-player) GHZ game reduces the value of the game to zero
polynomially quickly. That is, we show that the value of the
n-fold parallel repetition of the GHZ game is at most n^{-...
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 to
the...
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 equations...
This talk is based on a joint work with Thomas Kragh. Using the
generating function theory we split inject homotopy groups of
pseudo-isotopy and/or h-cobordism spaces into various spaces of
Legendrian manifolds, e.g. the space of Legendrian unknots...
For a polynomial f∈ℚ[x], Hilbert's irreducibility theorem
asserts that the fiber f−1(a) is irreducible over ℚ for all values
a∈ℚ outside a "thin" set of exceptions Rf. The problem of
describing Rf is closely related to determining the
monodromy...
For the Bargmann--Fock field on Rd with d>2, we prove that
the critical level lc(d) of the percolation model formed by the
excursion sets {f≥l} is strictly positive. This implies that for
every l sufficiently close to 0 (in particular for the nodal...
