Seminars Sorted by Series

The physicist Abrikosov predicted that in certain superconductors, one should observe triangular lattices of vortices, now called Abrikosov lattices.  When studying ground states of Coulomb gases, which is motivated by questions in approximation...

Humans tend to be better at physics than at mathematics.  After all, when an apple falls from a tree, there are more people who can catch it—they know physically how the apple moves—than people who can compute its trajectory from a differential...

A fundamental problem in the theory of compressible fluid is to provide a precise description of shock formation and development from smooth initial data. In this talk, I will present recent work in collaboration with Drivas, Shkoller and Vicol on...

I will present an elementary introduction to the regularity/uniqueness issues for the Navier-Stokes equations. Thanks to the convex integration technique, the h-principle is starting to take shape for the uniqueness problem. It might be possible...

We consider variational principles related to V. I. Arnold's stability criteria for steady-state solutions of the two-dimensional incompressible Euler equation. Our goal is to investigate under which conditions the quadratic forms defined by the...

I will explain a proof of a joint with D. Alvarez-Gavela and D. Nadler theorem which allows to make a Lagrangian submanifold transverse to a given Lagrangian distribution in exchange for making them piecewise smooth with canonical singularities...

Complexity of the geometry, randomness of the potential, and many other irregularities of the system can cause powerful, albeit quite different, manifestations of localization, a phenomenon of sudden confinement of waves, or eigenfunctions, to a...

Floer homology is a fundamental construction relating dynamical properties of Hamiltonian flows on symplectic manifolds to the topology of the manifold. Although this construction is global in nature, when the Hamiltonian flow is supported on a...

The incompressible 3D Euler equations have total kinetic energy conservation for smooth (spatially periodic) solutions. In the recent resolution of the Onsager conjecture by Isett, on the other hand, below certain threshold Hölder regularity, Euler...

An immersion from a smooth n-dimensional manifold $M$ into $R^q$ is called totally nonparallel if, for every pair of distinct points $x$ and $y$ in $M$, the tangent spaces at $f(x)$ and $f(y)$ contain no parallel lines. The simplest example is the...

In this talk, I will discuss joint work with Tristan Buckmaster, Nader Masmoudi, and Vlad Vicol in which we construct non-conservative solutions to the Euler equations which belong to the regularity class $C^0_t H^{1/2-}_x$. The motivation for such...

Lagrangian cobordism induces a preorder on the set of Legendrian links in any contact 3-manifold. We show that any finite collection of null-homologous Legendrian links in a tight contact 3-manifold with a common rotation number has an upper bound...

The talk will be devoted to explain how to construct weak solutions to 3D Ideal MHD equations obtained by convex integration (in the non smooth regime). We will show the existence of bounded weak solutions dissipating energy and cross helicity but...

We will discuss the regularity properties and size of generic level sets of functions that satisfy weak local Lipschitz conditions.

The non-resistive electron magnetohydrodynamics (MHD) has some peculiar connection with the Euler equation. Some one-dimensional reduced models are suggested as an attempt to build intuition toward understanding the nonlinear structure and dynamics...

I will present a recent result jointly with Francisco Gancedo (Universidad de Sevilla) and Huy Q. Nguyen (University of Maryland), in which we obtained the global well-posedness for the 2D one-phase Muskat problem with arbitrary large Lipschitz...

We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the...

We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations.  Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby...

Index theory goes back to Atiyah and Singer and deals with elliptic operators on Riemannian manifolds. It has numerous applications in geometry, topology, mathematical physics and other fields. On a Lorentzian manifold, naturally associated...