2019

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.

Since a couple of decades, Finsler geometry has been a very active field of research, with a particular stress on the use of purely metric methods in the investigation of various Finsler metrics that appear naturally in geometry, topology and convexity theory.

The Escuela Latinoamericana de Geometría Algebraica (ELGA) series of schools quickly became a major event for algebraic geometry in Latin America working as meeting point for the whole community due in part to the novelty of having some of the best researchers in our eld lecturing in Latin Americaf

The classical results and open problems that lie at the interface between commutative algebra and algebraic geometry, have undergone a striking evolution over the last quarter of a century, aided in large part by computer algebra calculations. At the heart of all these developments is the concept of syzygies: the analysis of the algebraic relations (syzygies) between the equations defining a geometric object leads to deep insights of its geometric properties.

For more than forty years, string theory has been able to impact in the development of several fields of mathematics. K- theory, algebraic and differential geometry, topology, infinite dimensional analysis, representation theory and derived categories, to mention a few, have been profoundly influenced by “stringy” ideas such as mirror symmetry, conformal field theory, D-branes and quantum cohomology. The main goal of this CIMPA Research School is to provide an introduction to many of these mathematical subjects as well as some background on string theory.

The school is organized around two thematic axes: Hopf algebras and tensor categories. The school is intended to introduce Ph.D. students and young researchers on both areas, to explain how they are interrelated, and also to present applications and new lines of research.

The courses on Hopf algebras aim to present the basics of this theory, the most relevant techniques and the classification program of finite-dimensional Hopf algebras. The theory of Nichols algebras will be presented, and how it fits into the classification program.