Program

Time: 4:30 - 5:30pm

Speaker: Jean-marc Delort

Time: 8 - 9pm

Speaker:Sasha Kiselev

Abstract
The question of how roots of polynomials move under differentiation is classical. Contributions to this subject have been made by Gauss, Lucas, Marcel Riesz, Polya and many others.  In 2018, Stefan Steinerberger derived formally a PDE that should describe the dynamics of roots under differentiation in certain situations. Interestingly, Dimitri Shlyakhtenko and Terry Tao have later formally obtained the same PDE as the evolution equation for free fractional convolution of a measure, an object appearing in free probability. The PDE in question is of hydrodynamic type and bears a striking resemblance to the models used in mathematical biology to describe collective behavior and flocking of various species - such as fish, birds or ants.  The equation is critical, but due to strongly nonlinear form of its coefficients, proving global regularity for its solutions is harder than for equations such as Burgers, SQG or Euler alignment model.  I will discuss joint work with Changhui Tan in which we establish global regularity of Steinerberger's equation and make a rigorous connection between its solutions and evolution of roots under differentiation for a class of trigonometric polynomials.

Time: 8 - 9pm

Speaker: Andrea Nahmod

Abstract
In this talk we focus on the time dynamics of solutions of periodic nonlinear Schrödinger with random initial data and the key underlying difficulty of understanding how randomness propagates under the nonlinear flow. We discuss the theory of random tensors, a powerful new framework that we developed with Yu Deng and Haitian Yue.

Time: 4:30 - 5:30pm

Speaker: Belkacem Said-Houari, Associate Professor, Mathematics, University of Sharjah

Abstract

We consider the Cauchy problem of a third-order in time nonlinear equation known as the Jordan—Moore-Gibson-Thompson equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. We show a local existence result in appropriate function spaces, and using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, we obtain polynomial decay rates in time for a norm related to the solution.

Time: 8 - 9pm

Speaker: Luis Vega, BCAM UPV/EHU Research Professor, Group Leader, La Universidad del País Vasco

Abstract
We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious non- linear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. Finally, we show that this behavior falls within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids.

Time: 9 - 10pm

Speaker: Emmanuel Grenier

Abstract
In this talk we review recent results on the instability of shear layers for the incompressible Navier Stokes equations as the viscosity goes to 0.

Time: 2 - 3pm

Speaker:  Boualem Djehiche, Professor of mathematical statistics, KTH Royal Institute of Technology

Abstract
Boualem will review some recent results on a problem of Mass Transport of Particles Towards a Target in a Brownian environment.

Time: 8 - 9pm

Speaker: Vlad Vicol, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University

Abstract
We discuss the formation of singularities (shocks) for the compressible Euler equations with the ideal gas law. We provide a constructive proof of stable shock formation from smooth initial datum, of finite energy, and with no vacuum regions. Additionally, for the non-isentropic problem, we show that sounds waves interact with entropy waves to produce vorticity at the shock. This talk is based on joint work with Tristan Buckmaster and Steve Shkoller.

Time: 9 - 10pm

Speaker: Edriss S. Titi, Arthur Owen Professor of Mathematics, Texas A&M University

Abstract
Large scale dynamics of the oceans and the atmosphere is governed by the primitive equations (PEs). It is well-known that the three-dimensional viscous primitive equations are globally well-posed in Sobolev spaces. In this talk, I will discuss the ill-posedness in Sobolev spaces, the local well-posedness in the space of analytic functions, and the finite-time blowup of solutions to the three-dimensional inviscid PEs with rotation (Coriolis force). Eventually, I will also show, in the case of “well-prepared" analytic initial data, the regularizing effect of the Coriolis force by providing a lower bound for the life-span of the solutions which grows toward infinity with the rotation rate.  The latter is achieved by a delicate analysis of a simple limit resonant system whose solution approximates the corresponding solution of the 3D inviscid PEs with the same initial data.

Time: 4:30 - 5:30pm

Speaker: Nejla Nouaili, Assistant Professor of Paris Dauphine University, Paris (UPD)

Abstract
In this talk Nejla will present a construction of  a solution for the Complex Ginzburg-Landau (CGL) equation in a general critical case, which blows up in finite time T only at one blow-up point. She will also give a sharp description of its profile. These is joint work with G.K.Duong and H.Zaag.

Time: 8 - 9pm

Speaker: Massimiliano Berti, Full professor of Mathematical Analysis at SISSA

Abstract
In this talk Massimiliano will present some new results about bifurcation of time quasi-periodic solutions for fluid equations

Time: 9 - 10pm

Speaker: Hajer Bahouri, Research Director of the National Center for Scientific Research at the University Paris-Est-Créteil-Val-de-Marne

Abstract
In this work, in collaboration with Galina Perelman, we prove that the derivative nonlinear Schrödinger equation is globally well-posed for general Cauchy data in $H^{\frac 1 2}(\R)$. The proof of our result is achieved by combining the profile decomposition techniques with the integrability structure of the equation.

Time: 4:30 - 5:30pm

Speaker: Anne-Laure Dalibard, Professor at Sorbonne Université

Abstract
The purpose of this talk is to present two 1d congestion models: a « soft » congestion model in which the congestion effects are described by a singular pressure law, and a « hard » congestion model in which the dynamics are different in congested zones (incompressible dynamics) and in the non-congested ones (compressible dynamics). For each model, we exhibit traveling fronts and investigate their stability. This is a joint work with Charlotte Perrin.

Time: 8 - 9pm

Speaker: Jose Carrillo, Professor of the Analysis of Nonlinear Partial Differential Equations

Abstract
The main goal of this talk is to discuss the state-of-the-art in understanding the phenomena of phase transitions for a range of nonlinear Fokker-Planck equations with linear and nonlinear diffusion. They appear as natural macroscopic PDE descriptions of the collective behavior of particles such as Cucker-Smale models for consensus, the Keller Segel model for chemotaxis, and the Kuramoto model for synchronization. We will show the existence of phase transitions in a variety of these models using the natural free energy of the system and their interpretation as natural gradient flow structure with respect to the Wasserstein distance in probability measures. We will discuss both theoretical aspects as well as numerical schemes and simulations keeping those properties at the discrete level.

Time: 9 - 10pm

Speaker: Charles Collot