Loss of compactness in nonlinear PDE: Recent trends (07w5087)

Objectives

The workshop has two main objectives. On the one hand, we would like
to bring together both experienced and young mathematicians in order
to illustrate recent/future lines of research. On the other hand, we
hope to stimulate the collaboration between mathematicians working
in this area since by nature the subject requires tools from many
different area of mathematics : tools from linear PDE, technics from
geometric measure theory, differential and Riemannian geometry,
topological methods from nonlinear analysis,...

We expect that every day of the workshop, one of the key experts
will give an extended talk on the overview of his field of
expertise. This extended lecture will be followed by more
specialized talks concerning recent progress as well as short talks
by young researchers participating to the workshop.

Our interest for this class of equations is largely motivated by the
study of vortices in various selfdual gauge field theories, of
conformal invariants in differential geometry, of the mean field
limit in statistical mechanics and by the connections with many
other contexts of theoretical physics, applied mathematics and
biology such as: gas combustion, thermionic emission and chemotaxis
process. Compactness properties are very interesting and yield to
global existence results. Moreover, there is a definite interest for
solutions "concentrated" at a set of given points, whose location
carries relevant information about the geometrical/physical
properties of the problem. For instance, in vortex theory it relates
to the presence of vortices with strongly localized electromagnetic
field. The last years have seen a large development of this area in
many directions and it will be a good time and opportunity to gather
many mathematicians to present the recent trends on these topics.