Weak KAM theory and PDE
             ============================
             Lawrence C Evans (Berkeley) 

This series of lectures will be a quick introduction to so-called
weak KAM theory, by which I mean the attempt to
exploit variational, dynamical systems and nonlinear PDE methods
to study ``integrable structures''  within Hamiltonian dynamics
in the large.

Lecture 1: Introduction, classical dynamics

In the first and elementary talk, I will explain about the Lagrangian
and Hamiltonian approaches to dynamics, changing  variables
to integrate the equations,  and connections with Hamilton-Jacobi PDE

Lecture 2: Dynamics methods

In the second talk, I will very briefly mention classical KAM theory and will
explain its generalization in the  variational and dynamical systems
methods of J. Mather and A. Fathi.


Lecture 3: PDE methods

I will finally discuss some new approaches, developed in joint work with
D. Gomes, based upon viscosity solution methods for Hamilton-Jacobi equations.
I will explain as well connections with the effective Hamiltonian introduced
by Lions-Papanicolaou-Varadhan.