I will discuss the construction of continuous solutions to the
incompressible Euler equations that exhibit local dissipation of
energy and the surrounding motivations. A significant open
question, which represents a strong form of the Onsager...
Joint work with Luc Hillairet (Orléans) and Emmanuel Trélat
(Paris). A 3D closed manifold with a contact distribution and a
metric on it carries a canonical contact form. The associated Reeb
flow plays a central role for the asymptotics of the...
In the last two decades great progress has been made in the
study of dispersive and wave equations. Over the years the toolbox
used in order to attack highly nontrivial problems related to these
equations has developed to include a collection of...
A vast array of physical phenomena, ranging from the propagation
of waves to the location of quantum particles, is dictated by the
behavior of Laplace eigenfunctions. Because of this, it is crucial
to understand how various measures of eigenfunction...
Korevaar and Schoen introduced, in a seminal paper in 1993, the
notion of `Dirichlet energy’ for a map from a smooth Riemannian
manifold to a metric space. They used such concept to extend to
metric-valued maps the regularity theory by Eells-Sampson...
Mean curvature flow (MCF) is a geometric heat equation where a
submanifold evolves to minimize its area. A central problem is to
understand the singularities that form and what these imply for the
flow. I will talk about joint work with Toby Colding...
Consider a point particle flying freely on the torus and
elastically bouncing back from the boundary of fixed smooth convex
obstacles. This is the celebrated Sinai billiard, a rare example of
a deterministic dynamical system where rigorous results...
In this talk, we will discuss some joint work with Alexandru
Ionescu on the nonlinear inviscid damping near point vortex and
monotone shear flows in a finite channel. We will put these results
in the context of long time behavior of 2d Euler...
The study of hyperkaehler manifolds of lowest dimension (and of
gauge theory on them) leads to a chain of generalizations of the
notion of a quiver: quivers, bows, slings, and monowalls. This talk
focuses on bows, their representations, and...
We consider a system of NN particles evolving
according to the gradient flow of their Coulomb or Riesz
interaction, or a similar conservative flow, and possible added
random diffusion. By Riesz interaction, we mean inverse
power ss of the distance...