Partial support of US participants is requests fund for an international conference in Nice France, which will be held from February 02 to 07, 2009. The Laboratoire J.A. Dieudonn´e of ?Universit´e de Nice-Sophia Antipolis? has graciously agreed to host that conference. This is the first international conference sponsored by the French National Research Agency (ANR) through a project named KAMFAIBLE. This conference will bring together leading experts from various continents (Europe, the United States of America and Latin America), who are expected to interact with postdocs and students. The workshop includes the participation of scientists from emergent nations such as Mexico, Brazil and the People?s Republic of China. The intellectual merit of this conference is to continue unearthing new connections between the weak KAM theory and other fields of mathematics such as dynamical systems, partial differential equations, optimal transportation theory, and many others. Another merit of this proposal is to continue exploring the ramifications of the weak KAM theory in many other subjects of sciences such as the homegenization theory, the kinetic theory of gases and fluids mechanic [GKP] [GNT2] (see also works in progress [GT1], [GT2]). This workshop will expose graduate students as well as faculty members to recent progress in the weak KAM theory, geometry and partial differential equations. The broader impact includes advancing knowledge, disseminating findings and exposing young researchers to this vibrant area at the crossing of Analysis, Riemannian Geometry, Dynamical Systems and Symplectic Geometry.