Differential Geometry: Theory and Applications

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:

• Theory of linearly and nonlinearly elastic shells;
• Relativity;
• Fluid Mechanics;
• Optimization of the shape of gears;
• Mesh optimization; etc.

On the other hand, it is expected that this School will strengthen or initialize scientific cooperations with developing countries from South-East Asia: India, Vietnam, Philippines, etc.