Tunisia

The aim of this school is to present precise and complete informations, which can be used immediately, on mathematical theories (quantization and harmonic analysis on non commutative groups), to students, who are finishing their master studies or are at the beginning of a thesis.

The ambition of this summer-school is to bring students and researchers in contact with 4 active fields whose common point is to be motivated by physics.

The nonlinear evolution equations have many applications, in particular in physics, chemistry and biology. This domain interests a wide mathematical community in the world. Besides the theoretical aspects, the modelling has numerous applications and became a major tool in nonlinear evolution equations. It is now considered as about an important domain of development. The various recent mathematical methods and the last most significant progress in this domain need to be exchanged and developed with the countries of North Africa, the Mediterranean Basin and the other nearby countries.

The modern Statistics and Probability Theory are domains of mathematics that need to be developped in North African and other African countries, as well research in these fields as their teaching. In addition to theoretical aspects, stochastic and statistical modelling have very numerous applications in other sciences, in economics and and in socio-economics. This modelling is an important factor of developpement.

L’organisation d’une telle école CIMPA est motivée par le potentiel et la qualité des étudiants chercheurs et des chercheurs dans le domaine du contrôle et de stabilisation des équations aux dérivées partielles qu’on a dans les pays du Maghreb et en particulier en Tunisie.

The theory of Dunkl had originated with the introduction by Charles Dunkl in 1989 of the Dunkl operators. At the same time, E.M. Opdam and G.I. Heckman and I. Cherednik have introduced similar operators by trigonometric methods. Since then, several mathematicians in the world became interested in this theory from several points of view. In particular, this theory is one of the major themes of research of "the school of harmonic analysis" in Tunisia. Several research studies have been published by Tunisian researchers in this field.

This Research School is intended for the study of Partial Differential Equations (PDEs) arising in geometry and physics. The major PDEs classes will be considered (elliptic, parabolic and hyperbolic), both for the construction of particular solutions and the classification of different qualitative behavior scenarios. Through the 6 courses, students will be given the opportunity to know the state of the art of the subject, with an introduction to the most recent techniques.

This school, organized from October 28th till November 9th 2013, focuses on the theme of Lévy and auto-similar processes which is a rapidly growing domain of the probability theory. Due to its various theoretical aspects (potential theory, classic and harmonic analysis, algebra, operator theory) and applications (physics equations, finance, insurances, dynamics of the populations…), this theme attracts numerous mathematicians from different fields.

Ces dernières années ont vu un renouveau de l’étude des graphes combinatoires par une approche issue de la physique mathématique, de la théorie du potentiel ou de la géométrie riemannienne. Cette École de recherche propose d’aborder ces questions avec :

Les conférences et cours proposés concernent trois communautés de chercheurs travaillant sur la modélisation du vivant par EDP par EDO (dynamique des populations, génomique, ... ) ou par Analyse Stochastique. Les cours concerneront aussi bien les aspects mathématiques et le développement de méthodes numériques que l’utilisation de la simulation numérique pour la compréhension des phénomènes biologiques.