2023

Differential equations are typically considered to be a subject of mathematical analysis or, more generally, "continuous mathematics". However, algebraic and discrete methods have been successfully applied to questions about differential equations such as, for example, finding symmetries or closed-form solutions. Recent years have witnessed significant development of constructive aspects of algebraic geometry and tropical algebra including deep theory and efficient algorithms.

La cryptographie post-quantique a pour objectif de développer des algorithmes mathématiques assurant la sécurité et résistant à l’ordinateur quantique. En effet, il est établi que si un tel ordinateur est mis au point, alors il permettra de casser de nombreux cryptosystèmes largement utilisés aujourd’hui comme RSA, ElGamal et d'autres. La communauté cryptographique a identifié 5 grandes pistes pour construire des cryptosystèmes résistants à l'ordinateur quantique. Elles exploitent la difficulté présumée de problèmes portant sur :

Coding theory is a remarkable example of how various areas of mathematics can be used to solve problems in the storage and transfer of information. In this school, participants will be introduced to various techniques used in recent years to solve problems in coding theory. The aim is to motivate participants to do research in coding theory.

The summer school aims at introducing students, junior faculty members, and young researchers to important theories and applications of data visualization, statistical and mathematical modeling, and various mathematical tools for model analysis.  There will be seven courses which will cover a variety of topics from data modeling to in-depth analysis and mathematical justifications for data-based decision making.

The school aims to introduce graduate students and young researchers to key topics in algebraic number theory and arithmetic geometry and their computational aspects. Modular forms and elliptic curves will be central, with a view towards Galois representations, complex multiplication and class field theory. Understanding of the abstract theory will be facilitated by an explicit and algorithmic approach, through an interactive approach where we will make use of freely available computer algebra systems.

Quantum computers threaten to break most of the cryptography we currently use to protect our information security systems. In a quantum computer, performing operations comes from a quan- tum physical notion that works differently from a classical computer setting, and it gives an expo- nential speed-up for certain computations. To construct quantum-resistant cryptographic systems, we need a new class of hard mathematical problems. Many of them are currently competing in the National Institute of Standards and Technology (NIST) Post Quantum Cryptography Standardizati- on.

As it is described in the title the CIMPA School on “Differential Galois Theory and Applications to Mechanics” will be devoted to the application of the differential equation coming from Mechanical problems using tools from differential algebra and specifically the Differential Galois group.

L'école de recherche CIMPA N'Djamena 2023 vise à initier les étudiants de master, doctorants et les jeunes mathématiciens aux outils mathématiques et statistiques pour modéliser les systèmes complexes. L'objectif est de préparer les participants à modéliser des problèmes concrets ancrés dans les réalités africaines en abordant les défis d'actualité tels que les maladies infectieuses, la sécheresse ou encore les effets de la migration humaine sur les écosystèmes.

A blockchain is a digital list of data records, comprised by blocks which are organized in chronological order and are linked and secured by cryptographic proofs.

It started to secure digital documents from data tampering, and quickly lead to the creation of Bitcoin, the first decentralized electronic cash system, or cryptocurrency.

The school aims to introduce graduate students and young researchers to the modern theory of non-associative algebras and their applications, with a focus on Lie algebras, Leibniz algebras, incidence algebras, genetic algebras and their deformations. The courses will be focused on some key topics in description of algebraic systems with certain properties, algebraic systems over positive characteristic, deformations of algebraic systems, classifications of algebraic systems.