2019

Le programme de l’école de recherche est orienté de façon à faire profiter les auditeurs des dernières avancées dans le domaine du Machine Learning, Deep Learning et d’autres techniques de réduction de modèles. La communauté de l’intelligence artificielle et des statistiques, et celle du calcul scientifique se sont retrouvées ces dernières années pour donner naissance à de nouveaux algorithmes utiles aux deux thématiques.

The notion of a group describes symmetry in mathematics. In recent decades, certain quantum mathematical objects have appeared whose symmetries are better described by group-like objects called tensor categories. Examples of areas of mathematics where tensor categories play a key role include subfactors, quantum groups, Hopf algebras, quantum topology and topological quantum computation. The aim of this is school is to introduce graduate students to tensor category theory and their applications to Topological Quantum Field theory, Subfactor theory and Hopf algebras.

This school is about a smooth transition from classical graph theory to modern approaches. At first extension of coloring results to homomorphisms of digraphs are presented. Next lectures would be on algorithmic graph theory with classic approaches such as LexBFS ordering being combined with modern ideas. Mixing algorithms with applications, there will be lectures on distributed algorithms. School will conclude by lectures on how to use power of randomness, which is a rather new modern and powerful method.

The school aims at presenting some of the current approaches in PDE modelling and mathematical analysis of biological phenomena or related domains. It aims at allowing the researchers and the students of Master’s degree level and talented undergraduate students to acquire a basic training in that field and to have an overview of what is the current research status of these types of problems.

Application of Dynamical Systems to Biology is nowadays an important challenge. The goal of this school is, on the one hand to present the basic tools in Dynamical Systems to solve ODE's, and, on the second hand, to present how these tools can be used in Biology. The school will comprise two series of lectures. One theoretical one and one for applied mathematics. A large part will be devoted to exercises sessions.

The primary objective of this summer school is to provide an opportunity for mathematicians and biologists in Nepal and neighboring countries to explore mathematical skills that can be applied to address issues of real-life biological systems. The summer school aims to introduce students, junior faculty members, and young researchers to the important theories and appli- cations of Mathematical Biology.

The theory of hyperplane arrangements is a modern and very active area of research. In the recent years there have been a huge progress this subject. At this CIMPA school, through 6 carefully selected courses, participants will be introduced to various aspects of Hyperplane Arrangements together with the main open questions that are still present in the area.

The school will present modern tools of number theory and algebra, with a focus on their use in cryptography. Although cryptography has a long history, it has developed during the 20th century into a modern science with the help of computer science and mathematical tools coming from algebra, number theory, combinatorics, geometry. The minicourses will present various aspects of the subject: elementary and algebraic number theory, elliptic curves, primality tests, representation theory, lattices, computational aspects, applications to cryptography.

Les Probabilités et statistique sont en forte carence en Algérie et aussi dans les pays voisins. Cette discipline est abordée dans plusieurs masters Algériens dont un de l’analyse stochastique et Applications. Ces formations ont souvent besoin de faire appel à des compétences étrangères intervenant sur de courtes durées avec les contraintes pédagogiques que cela entraîne. Cette école veut attirer de nouveaux doctorants et accélérer la formation de jeunes docteurs spécialisés en Probabilités et Statistique.

The aim of this is school to introduce the participants to the arithmetic and computational aspects of the theory of elliptic curves.

We will develop the theory of elliptic curves from its very beginning also providing an introductory course on algebraic curves and the Riemann Roch theorem. Topics that will be covered include: basic geometric and arithmetic results for elliptic curves over number felds and over fnite felds, the Mordell- Weil theorem for elliptic curves, Galois representations attached to elliptic curves, and the Birch and Swinnerton Dyer Conjecture.