China

On the one hand, it is planned to give a thorough presentation of the basic notions of Differential Geometry: metric tensor, Riemann curvature tensor, fundamental forms of a surface, covariant derivatives, fundamental theorem of surface theory, etc. This field is indeed often considered as a "classical" one, but it has been recently "rejuvenated", thanks to the manifold applications where it plays an essential role. Some of these applications will be studied in the School, such as:

The topics of this school are related to nonlinear analysis and asymptotic analysis of partial differential equations arising from geometry and physics. They include: KAM theory of infinite dimensional dynamic system and applications in PDE, critical blow-up of nonlinear Schrodinger equation, integral system and variational methods in differential geometry , semi-classical analysis and theory of resonances of Schrodinger equation. The objective of these mini-courses at the level of French DEA is to introduce moden tools and present recent progesses in these fields.

The research school is intended to higher education and research teaching staffs. The expected audiences are PhD students, young faculty members from universities in Asia.

Predicting the evolution of geophysical fluids ( atmosphere, ocean, continental waters ) is an important social issue especially for countries with a strong potential to undergo extreme natural events (tornados, typhoons, flood) with severe impacts on the economical and social activities).

These last decades strong improvements have been realized in modelling these flows and reliable models now exist for predicting natural catastrophes related to geophysical flows.

The Ginzburg - Landau equation is a nonlinear partial differential equation which was proposed around 1950 in the modelling of superconductors. Since then, it has become an extremely popular tool in many other areas of physics where vortices and/or topological defects appear, e.g. superfluids; new problems in physics with a similar flavour arise constantly e.g. ferromagnetism, Bose-Einstein condensates etc.... Starting around 1990, there has been remarkable progress in the mathematical understanding of such equations.

The objective of the school is to give an initiation to the modern theory of plates and shells, including in particular the use of asymptotics methods for the justification of bidimensional models, the mathematic analysis of these models and the study of the most performing methods employed in numerical simulations. The school is intended to young researchers and students with a good training in fonctional analysis, partial differential equations and numerical analysis.

The objective is to provide the audience with modern mathematical methods in the framework of both stochastic and contingent dynamics of economic anf financial markets, discrete, continuous and hybrid. The respect at each moment and for each stochastic event of scarcity constraints is the main unifying and federative objective of the mathematical methods proposed. Specialists of stochastic and viability techniques will confront their view points together with practioneers.

The objectives are to present an outline of the recent development of the application of Partial Differential Equations to Image Processing. These last 10 years have seen a new field emerging from a need for better mathematical formalism of problems in Image Processing. It was introduced at first for an invariant image analysis through different scales, and also used for adaptative image smoothing, image sequence analysis, active contours and surfaces, curve evolution.

The objective of this school is to train young scientists in developing countries by presenting recent results on the subject in systematic way and pointing out some important research directions in the future.

The objective is to train young scientists and introducing them to recent development of analysis and geometry on complex homogeneous domains.