New developments on variational methods and their applications

The subject has come of age in the last forty years, and a number of surveys and monographs have described much of the progress. A first objective is obviously to discuss some of the recent developments while emphasizing new applications to nonlinear problems.

However, more often than not, progress is driven by specific applications. Novel variational techniques developed by groups or individuals concerned with these applications, do not make their way to others who may be using similar variational methods but on different type of problems. This workshop will bring together experts and young researchers working in different areas of variational methods. These areas include abstract variational methods such as Novikov Morse theory and nonsmooth critical point theory, geometric PDEs, and nonlinear problems from applied fields such as superconductivity and phase transitions. So the second objective of the workshop is to provide an opportunity to exchange ideas from abstract theories and applications so that novel variational methods can find more applications and new theories can be developed. Below are the main themes of the workshop:

1. General theories: Novikov Morse theory and nonsmooth critical point theory.

Novikov Morse theory studies Morse theory for multiple valued functions. It has important applications in geometry, mechanics, and physics; in particular, differential forms, motions in elctric magnetic field and the Chern Simons functional etc. Nonsmooth critical point theory extends the critical point theory from differentiable functions on differential manifolds to continuous functions on metric spaces. There are several applications in the literature, and it is expected to have more applications in very diverse fields.

2. Variational methods in phase transitions, vortex dynamics and superconductivity.

Many problems in these applied areas can be studied by variational methods. Indeed many new ideas such as the renormalized energy method, new reduction methods, new perturbation methods have been developed recently through the study of individual problems in these areas. Variational methods give a very good understanding of physical phenomena such as concentration, vortex formation and their dynamics.

3. Variational methods in Geometry

Many variational problems arise in geometry particularly in the study of Kahler-Einstein manifolds, minimal surfaces, scalar curvature, harmonic maps, etc. This area is very active and has been a major source of new ideas in variational methods.

Confirmed Participants

Programme (PDF file)

Abstracts (PDF file)

Videos

Report (PDF file)