Tours, France      
Summer school on
"Geometric methods for
PDEs and dynamical systems"

ANR Weak KAM beyond Hamilton-Jacobi

Porquerolles, France
June 8-12, 2015

Young researchers are encouraged to apply for grants to attend the summer school. We plan to schedule several short talks or poster sessions. If they are interested they should send a CV and an abstract to


List of participants

How to reach the Island of Porquerolles

The simplest option is to go to Marseille (either by train to Saint-Charles station or by plane to the Marseille-Marignagne airport). Then take a train from Marseille to the city of Hyeres (tickets can be booked on the SNCF website). Finally, take a bus to Tour Fondue, which is the port of Hyeres where you can find the boats for the island. The schedule of the boats can be found at this website.

  • Determinantal Point Process, Alexander Bufetov (I2M CNRS)

    Determinantal point processes naturally appear in many problems of representation theory, asymptotic combinatorics and mathematical physics, especially, the theory of random matrices. They have recently become an extremely active area of research. The course will give an elementary introduction to determinantal point processes. Some open problems will be formulated.

  • Gene Wayne (Boston University)

    Lecture 1: The Oseen vortex
    This lecture will focus on the Oseen vortex, an explicit solution of the two-dimensional Navier-Stokes equation.  Using methods from dynamical systems theory I will explain how one can prove that any solution of the Navier-Stokes equation whose initial vorticity distribution is integrable will asymptotically approach an Oseen vortex.  These are results originally obtained in collaboration with Th. Gallay.

    Lecture 2: Vortex models for two-dimensional viscous flows
    Building on the classical point vortex models of inviscid  two-dimensional fluids and utilizing the insights from Lecture 1 I will describe how one can develop models which systematically incorporate viscosity and finite core size of the vortices.  These models also lead to new computational models for studying two-dimensional fluids.  These
    results were originally obtained in collaboration with A. Barbara, R. Nagem, G. Sandri and D. Uminsky.

    Lecture 3:  Classical mechanics and point vortex methods
    Returning to the classical point vortex model I will explain its interpretation as a classical mechanical Hamiltonian system and explain how techniques originally developed to study the N-body problem in celestial mechanics can be modified to prove the existence of new classes of solutions of the point-vortex model, and also to analyze the stability of these solutions.  This is joint work with A. Barry and G.R. Hall.

  • Nonlocal problems and applications, Enrico Valdinoci (Berlin)

    We would like to consider some nonlocal problems of fractional type that arise in differential equations and geometric measure theory. In particular, we would like to discuss the following topics:
    • Nonlocal phase transition equations: symmetry, rigidity, density estimates and asymptotics;
    • Nonlocal minimal surfaces: regularity and asymptotics;
    • Nonlocal Schroedinger equation: motivations and concentration phenomena;
    • Crystal dislocations: the Peierls-Nabarro model, macroscopic behavior, attractive and repulsive potentials, dislocation dynamics.

  • Ergodic optimization and joint spectral radius, Oliver Jenkinson (London)

    This course will cover various aspects of ergodic optimization (i.e. the study of optimizing ergodic averages), with particular emphasis on applications to joint spectral radius problems.

ANR KAM Faible