CONFERENCE

PDE/Probability Interactions:
Kinetic Equations, Large time and Propagation of Chaos

April 18 – 22, 2017

The objective of this conference is the study of the convergence of large interacting particle systems towards classical non linear physical equations, such as the Boltzmann equation, Landau equation, Keller-Segel equation, Cucker-Smale equation, etc. We will focus in particular on the convergence (as the number of particles increases to infinity), enabling to quantify the non linear approximation and its simulation, as well as its time uniformity.

We will thus also focus on the long time behaviour of both the particle system and the non linear equation. We will consider difficult and particularly relevant models with singular interactions (coulombian potential, inhomogeneous Boltzmann or Landau, etc).

This conference will bring together international specialists of both PDE and probability theory and by confronting these two fields, we hope to conceive new methodologies enabling us to tackle these hard problems.

This conference will be jointly organized by the ANR projet Stab (Stabilité du comportement asymptotique d’EDP, de processus stochastiques et de leurs discrétisations) coordinated by Ivan Gentil and François Bolley, whose main aims essentially coincide with the subject here.


Scientific Committee

Eric Carlen (Rutgers University)
José Antonio Carrillo (Imperial College London)
Patrick Cattiaux (Université de Toulouse)
François Golse (
Ecole polytechnique)
Laure Saint-Raymond (Université Pierre et Marie Curie)

Organizing Committee

François Bolley (Université Pierre et Marie Curie)
Nicolas Fournier (Université Pierre et Marie Curie)
Arnaud Guillin (Université Blaise Pascal Clermont-Ferrand)
Clément Mouhot (University of Cambridge)

Senior Talks 

Entropy production in nonlinear recombination models   (pdf)

Coarse-graining of collective dynamics models – Metric vs topological interactions (pdf)

On the stability and the applications of interacting particle systems   (pdf)

A coupling approach to the kinetic Langevin equation   (pdf)

Asymptotically stable particle in cell methods for the Vlasov-Poisson system with a strong external magnetic field

Quantitative uniform propagation of chaos for Maxwell molecules   (pdf)

The Cauchy problem for the quantum Boltzmann equation for bosons at very low temperature​   (pdf)

The isotropic Landau equation   (pdf)

Propagation of chaos for the 3D homogenous Landau equation with moderalty soft potential

On a stochastic particle approximation of the Keller-Segel equation

Metastability : a journey from stochastic processes to semiclassical analysis 
(pdf) (LJ7direct.mov)

Long time behaviour of some McKean-Vlasov equation with non-convex connement potential

On Markov intertwinings

Villani’s program on constructive rate of convergence to the equilibrium : Part I – Coercivity estimates   (pdf)

On the Propagation of Chaos in Kinetic Theory   (pdf)

Asymptotic behaviour for homoenergetic solutions of the Boltzmann equation(pdf)

Mini-courses

From hard-sphere dynamics to the Boltzmann equation

Entropic structure of the Landau equation with Coulomb interaction   (pdf)

Junior Talks 

Long-time behaviour of the Landau equation

Entropic Ricci curvature on discrete spaces  (pdf)

Propagation of chaos for Holder continuous interaction kernels via Glivenko-Cantelli   (pdf)

Mean field kinetic particles and the Vlasov-Fokker-Planck equation   (pdf)

Flocking for stochastic variations of the Cucker-Smale model   (pdf)

Convergence rates for a particle approximation of conservation laws   (pdf)

Propagation of chaos for aggregation equations with no-flux boundary conditions and sharp sensing zones   (pdf)

On the Boltzmann equation without cutoff   (pdf)