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
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
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: 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: 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
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: 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: 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...
**Limited seating is available in Simonyi Lecture Hall and is by
invitation only for IAS members or faculty. Remote access will be
given to those that register. Please contact Naomi Kraker at
receive the zoom link for the...