Wavelets And Multifractal Analysis in Cargèse 2004

We wish to thank the following for their contribution to the success of this conference: European Office of Aerospace Research and Development of the USAF - National Science Foundation - Centre National de la Recherche Scientifique - Direction Générale de l'Armement - Office of Naval Research International Field Office - Institut National de Recherche en Informatique et Automatique

Wavelet And Multifractal Analysis 2004

Summer School
IESC

Institut d'Études Scientifiques de Cargèse IESC

Corsica, France

July 19 - 31, 2004

This event will focus on two topics: wavelets (and its numerous variations) and multifractal analysis. Both themes evolved towards self contained theories, and yet, a host of reasons justify for coupling them in a same training course. Firstly, both analyses share the same conceptual backbone of "scale" : it is the "mathematical zoom" commonly associated to wavelet analysis and it is the "scaling laws" that underlie multifractal structures. Very naturally then, wavelets stood as a privileged tool for analyzing and characterizing multifractal signals. In the course, both disciplines tended to merge and give rise to a truly crossover research activity. From an historical viewpoint, publication in 1984 of the article by A. Grossmann and J. Morlet, "Decomposition of Hardy functions into square integrable wavelets of constant shape" really launched the wavelet business with its extraordinary expansion. The 20th anniversary date in 2004 is timely to depict state of the art and to present current advanced results in a still vivid domain, but also to think about forthcoming developments and challenges. This will constitute the guideline for the first school theme, organized in 90 minutes courses covering the theoretical and applied aspects. A clear endeavour is to favour the inter-disciplinary side and to renew the broad scope spirit of first wavelet conferences.
The second school topic will be devoted to Multifractal analysis. Initially derived in physics, it provided with a theoretical framework allowing for interpreting fully developed turbulence signals. Often associated to wavelets, this description is now widely adopted in a host of applications (physics, geophysics, biology and bioinformatics, network tele-traffic, astronomy, economics,…). Although multifractals and wavelets communities kept interacting all along, counterpart of this success stems from a research efforts dispersion, and a confusion with respect to the applicability of some theoretical results. Conversely, issues whom answers would constitute major breakthroughs, remain unexplored. This week will gather scientists from different domains, multifractal analysis theorists and users will strive for assessing useful results and for itemizing opened questions. We programmed to start with a long course (4H30) to introduce fundamentals, followed by a series of 90 minutes courses taught by mathematicians, physicists, signal and image processing specialists.

As Wavelets and Multifractal themes are still at present, very fast-moving areas of research, no proceedings will be published. Lecture notes will be distributed to participants on paper hardcopies. At the same time, all speakers will be requested to post on the Web site of the event [http://wama2004.org] their transparencies or the text of their presentations, accessible for the benefit of the scientific community at large. The posters and presentations of the trainees of their own work will also be eligible for on-line publication in the same Web site.

All participants are invited to contribute to Connexions: Sharing Knowledge and Building Communities.