Previous Conferences & Workshops

Abstract: I will discuss some questions related to turbulence.

The study of nodal sets, i.e. zero sets of eigenfunctions, on geometric objects can be traced back to De Vinci, Galileo, Hook, and Chladni. Today it is a central subject of spectral geometry. Sturm (1836) showed that the n-th eigenfunction of the...

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

Abstract: The incompressible porous media (IPM) equation describes the evolution of density transported by an incompressible velocity field given by Darcy’s law. Here the velocity field is related to the density via a singular integral operator...

Abstract:   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...

Abstract. I will describe a new geometric approach for the shock formation problem for the Euler equations.   A complete description of the solution along the hypersurface of first singularities or preshocks will be given.

A nodal domain of a Laplacian eigenvector of a graph is a maximal connected component where it does not change sign.  Sparse random regular graphs have been proposed as discrete toy models of "quantum chaos", and it has accordingly been conjectured...

Abstract: The quadratic Monge optimal transportation problem can be revisited in Euler's language of Hydrodynamics as was explained by Jean-David Benamou and the speaker about 20 years ago. It turns out that Einstein's theory of gravitation, at...