# Video Lectures

The viscosity of a fluid is usually a constant, independent of the stress. There are however in nature several examples of fluids (ice, molten lava, blood, certain polymers, some salt solutions) where viscosity changes under applied forces. Such...

A key discovery from the past six decades of solar system exploration is that liquid water oceans may be a common planetary phenomenon. At least six ice-covered moons of the outer solar system present compelling evidence for subsurface oceans, and...

We discuss recent mathematical constructions of self-similar gravitational collapse for Newtonian stars governed by the Euler-Poisson system, known as Larson-Penston solutions for the isothermal stars and Yahil solutions for polytropic stars, and...

It is known since the work of Dyachenko & Zakharov that for the weakly nonlinear 2d infinite depth water waves, there are no 3-wave interactions and all of the 4-wave interaction coefficients vanish on the non-trivial resonant manifold. In this...

The lecture will discuss a joint work with Gregorio Baldi and Bruno Klingler. Given a polarized Z-VHS over a complex, smooth quasi-projective variety S, we describe some properties of the Hodge locus, a countable union of algebraic subvarieties of...

In this talk we consider the pressureless Euler system in dimension greater than or equal to two. Several works have been devoted to the search of solutions which satisfy the following adhesion or sticky particle principle: if two particles of the...

In this talk we will present a construction of global existence of small solutions of the modified SQG equations, close to the disk. The proof uses KAM theory and a Nash-Moser argument, and does not involve any external parameters. We moreover prove...

Let M be a smooth manifold in an Euclidean space; consider the motion of a material point on M in absence of friction. The D'Alembert Principle says that the acceleration vector is orthogonal to the tangent space to M, and this fact defines the...

I will discuss some questions related to turbulence.

We consider the density properties of divergence-free vector fields b∈L1([0,1],\BV([0,1]2)) which are ergodic/weakly mixing/strongly mixing: this means that their Regular Lagrangian Flow Xt is an ergodic/weakly mixing/strongly mixing measure...