Lebanon

This school will present various aspects of the theory of algebraic curves, as a way of introducing students, as well as researchers not specializing in these fields, to the areas of algebraic geometry and arithmetic geometry. A related goal is to assemble a regional network of mathematicians working in algebra, number theory, and algebraic geometry. The school also aims to promote collaboration between mathematicians from the region and research teams in Europe, both on the level of joint research projects and in shared advising (co-advising) of thesis students.

The organization of this school is motivated by the promising potential and the good scientific level of students and young researchers in the field of differential geometry in Lebanon and in the neighboring countries (Iraq, Jordan, Syria ..). The school aims to be a unifying project for young researchers in Lebanon who recently graduated a PhD in the field of differential geometry, and thus facilitate the emergence of a research team on this issue in Lebanon.

This is a CIMPA-UNESCO School.

La Théorie des Graphes se situe à l’interface de la combinatoire et des mathématiques discrètes. C’est une thématique en plein essor ces dernières décennies et en évolution constante tant du point de vue recherche que du point de vue applications. dans différents domaines tels que l’étude de réseaux, l’informatique, les probabilités , la biologie .... L’étude de ces graphes a donné lieu à des résultats spectaculaires en combinatoires ces dernières années comme par exemple la résolution du problème des graphes parfaits.

Interactions between analysis and geometry are of considerable importance in mathematics. The famous Yamabe problem and Perelman’s proof of Poincaré are remarkable illustrations of these interactions. The aim of this school is to provide an introduction to some of these topics, focusing on geometric problems that are expressed in terms of elliptic equations.

Graph Theory lies on the interface between combinatorics and discrete mathematics. The domain has expanded considerably over the last decades with interactions invarious fields such as the study of social networks, algorithms, computer science, interprobabilities, discrete geometry, producing some spectacular results.

Graph Theory lies on the interface between combinatorics and discrete mathematics. The domain has expanded considerably over the last decades with interactions invarious fields such as the study of social networks, algorithms, computer science, interprobabilities, discrete geometry, producing some spectacular results.

The relation between modular forms and their corresponding L-functions with various disciplines of mathematics has undergone significant evolution in the past century due to the critical role these complex analytical functions play in resolving essential problems and conjectures. The connection of modular forms and their L-functions with number theory, elliptic curves, representation theory, and algebraic geometry, among others, have resulted in diverse generalizations in different directions.

Two centuries after its origin, Complex Analysis remains a vi- brant and fruitful field of research. Its applications go well beyond the realm of Mathematics and range from Physics to Engineering. Current research in Complex Analysis blends techniques from a variety of Mathematical areas and thus requires a broad expertise. Following this philosophy, the school will expose students to a wide spectrum of fields interacting with Complex Analysis. Special emphasis will be put on Differential Geometry, Partial Differential Equations, Dynamical Systems and Algebraic Geometry.