07w5087 Loss of compactness in nonlinear PDE: Recent trends

Arriving Sunday, August 26 and departing Friday, August 31, 2007

Organizers: Pierpaolo Esposito (Universitaegli Studi Roma Tre), Frank Pacard (Université Paris 12-val de Marne), Gabriella Tarantello (Universita' di Roma Tor Vergata).

Confirmed Participants

Press Release: Leading Nonlinear Analysts at BIRS

Information for Participants

Schedule and Abstracts (PDF file)

Final Report (PDF file)

Workshop Videos

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.