Many studies have been carried out in a dozen institute in the general area of differential geometry. More specifically, the projects can be grouped into 4 areas:

Variational problems: submanifolds of prescribed mean curvature; harmonic maps; qualitative behaviour of minimizers.

Spectral theory: eigenvalue estimates in the compact care; spectral analysis in non compact manifolds; isoperimetric inequalities.

Prescribing geometric data: non positively curved manifolds; pinching theorems; scalar curvature or mean curvature; Kaehler, hyperkaehler and quaternionic geometrics.

Theoretical physics: nonlinear sigma models; supersymmetry; anomalies; twistors.
Global Differential Geometry is a rapidly growing field, due to its strong interactions with other subfields of mathematics and other sciences. Its notions and techniques are now widely used in many other areas, a recent spectacular success being the new results in the differential topology of 4 dimensional manifolds. Most of the recent achievements in differential geometry rely heavily on solving somelinear and non linear partial differential equations. On the other hand geometry has enriched the theory of partial differential equations with specific problems which turned out to be landmarks. This project aims at enhancing contacts between three schools of differential geometers (those keen on PDE techniques, those interested in ideas borrowed from physics and those with a more geometric training). It is organised according to four main themes : variational problems, spectral theory, prescribing geometric objects and new developments induced by theoretical physics.