2025

An $L$-function is a function defined additively by a Dirichlet series with a multiplicative Euler product.
The initial work of Dirichlet was generalized to number fields by Hecke and given an adelic interpretation by Tate
which paved the way to move from $GL(1)$ to higher degree $L$ functions associated to automorphic forms of $GL(n)$ for a general n .

The school aims to introduce graduate students and young researchers to modern algebra and its applications, with a focus on Tits-Kantor-Koecher construction, Jordan algebras, Rota-Baxter Lie algebras and some non-associative algebras, such as Lie algebras, Jordan algebras, automorphisms, derivations and cohomology of classical and quantum algebras and their applications in other areas of mathematics. The courses will deal with a description of certain algebraic systems, their classifi cation, and their connection with other algebraic systems.

The purpose of the school is to present a self-contained proof of a famous theorem of Serre in 1972. This theorem tells us that the representation associated to the Galois action on the p-torsion points of an elliptic curve is surjective for p great enough. This theorem had a very great impact in the field of arithmetic geometry and opened the field to numerous problems that are, for some, still open today. After introducing the students to the topics needed to understand the proof, illustrating the theory through exercises and sessions on computer, we will present the proof itself.

Les activités scientifiques prévues sont organisées sous forme de cours, travaux dirigés et travaux pratiques. On prévoit éventuellement des tables rondes (une ou deux) autour de la thématique de l’école le soir. La thématique s’articule autour de quelques outils mathématiques qui interviennent en intelligence artificielle. Il s’agit des statistiques, optimisation linéaire, analyse numérique.

Mathematical modelling in biology and related domains is becoming of increasing importance in the mathematical community as well as for biologists, physicians, engineers in environmental science from the point of view of possible applications.
The recent progress in the development and the analysis of these mathematical models have to be shared with Cuba and other countries of the Caribbean area.

The aim of this CIMPA school will be to familiarise graduate students and young researchers with the field of enumerative and analytic combinatorics, and to show its many connections to other areas, especially computer science.

Les mathématiciens sont sollicités par les médecins pour l’optimisation du traitement de maladies gravesoude gestes opératoires, par les généticiens pour le séquençage du génome, etc.
Cette école CIMPA a pour vocation de former des étudiants de masters et des jeunes chercheurs mathématiciens modélisateurs pouvant s’impliquer dans des secteurs d’activités variés.
Elle est caractérisée par une forte interaction entre cours fondamentaux et appliqués, ce qui permet de rassembler les connaissances théoriques et pratiques sur un problème concret.

The main focus of the school will be the mathematics around the L-functions and modular forms database (LMFDB). It will introduce the students to the main ideas and philosophies around modularity theorems, which connect algebraic curves and abelian varieties on one side with modular forms and L-functions on the other. Theoretically, such ideas are part of the Langlands program; the LMFDB can be seen as a way to make this program accessible and concrete by means of a huge treasure trove of examples.

L’école CIMPA Théorie des représentations et ses applications à la physique aura lieu durant deux semaines à Ouagadougou offrira une introduction aux méthodes modernes de la théorie des représentations et explorera ses applications en physiques. Deux cours de bases initieront les concepts de base de la théorie des représentations et cinq cours spécialisés présenteront plus en détails le calcul diagrammatique, les dualités de Schur-Weyl et les invariants quantiques et exploreront leurs applications en physique. Plusieurs ateliers animés par des experts et expertes du domaine seront offerts.

From September 08-19, 2025, the University of Douala of Cameroon (through the Faculty of Science) and the Technical University of Braunschweig of Germany (through the Computational Sciences in Engineering study program and the Center for Mechanics Uncertainty and Simulation in Engineering) will co-organize (with the contribution of Advanced Sciences and Technology Academy, a private Institution in Douala) a CIMPA Summer School at the University of Douala on the topic «On Modern Mathematical Tools in Mechanics ».