Algeria

Geometry and Dynamics

The general theme of this school lies at the intersection of geometry and dynamics, focusing on the interactions between Riemannian and Lorentzian geometries on the one hand, and dynamical systems on the other. For instance, a Lorentzian, Riemannian, or more generally semi-Riemannian metric naturally gives rise to dynamical objects such as:
• the action of its isometry and conformal groups,
• the geodesic flow (a differential equation on the tangent bundle), and
• the Ricci flow (an evolution PDE on the space of all metrics).

Numbers Theory

Francesco Pappalardi

Summary:

Elementary Numbers Theory:

Quadratic reciprocity
Arithmetic fonctions

Analytic Numbers Theory :

Dirichlet Arithmetic progression
Prime Number Theorem

Integrable systems

Maciej Dunajski

Summary: Integrable systems are nonlinear differential equations which ‘in principle’ can be solved analytically. This means that the solution can be reduced to a finite number of algebraic operations and integrations. Such systems are very rare - most nonlinear differential equations admit chaotic behaviour and no explicit solutions can be written down. Integrable systems nevertheless lead to a very interesting mathematics ranging from differential geometry and complex analysis to quantum field theory and fluid dynamics.

Algebraic curves over finite fields

Lecturer: Christophe RITZENTHALER

Abstract

This mini-course is a motivated introduction to the problematic of number of rational points on curves over finite fields. It will serve as a pretext to introduce the basics of algebraic geometry (Nullstellensatz, projective geometry,...) with a far-away open problem in mind (distribution of the number of points on genus 4 curves). We will in particular try to reduce the number of coefficients of these curves to be able to run some experiments with a computer.

EMA Dynamique collective, systèmes couplés, et applications en biologie/écologie

Coordinator: Daniel Massart (Université de Montpellier, France)

Divers aspects des surfaces

Coordinators: Hacen Zelaci (zelaci-hacen@univ-eloued.dz) & Adrien Boulanger, Aix-Marseille Université, France (adrien.boulanger@univ-amu.fr)

Mathematical models for water flows and water refining

The objectives are to promote the international cooperation between the Maghreb, the Sahel, and the north of the Mediterranean sea, in the domain of water flows and wastewater treatment.

Riemannian and Pseudo-Riemannian Geometries and Dynamics and Applications

The aim of the school is to provide a thorough description of the interactions between geometry (with its different branches) and dynamical systems, in one part, and between these two disciplines and different extra-mathematics areas of research (General Relativity, Cosmology, Black Holes, ……), in other part. A pedagogical treatment of the subjects, at both the introductory and advanced level, will be provided in the form of a series of lectures by individual speakers, ranging from evolutions of the subject till the most recent developments.

Nonlinear Control and Applications

The aim of the school is to expose the recent results in nonlinear control theory and to present some applications in robotics and in bioprocess. During the school will hold a symposium on Automatics and Dynamical Systems in which participants could expose their research.

Contrôle géométrique, stochastique et des EDP

The goal of this school consists of promoting to the scientific north-african community the modern tools of geometric control theory coming both deterministic and stochastic frameworks used in finite and infinite dimension. Emphasis will be made on applications of control theory, especially to the economic field. The scientific content of the school is divided in two distinct parts : the first one is devoted to nine courses of six hours each.

Algeria