2020

The school is intended for students in mathematics, physics and engineering, graduate or undergraduate in the late years of their bachelor. The participants will be offered geometric notions of some mathematical theories useful for understanding problems related to mechanics and control theory. The programme of the school consists in 7 courses of 6 hours each, lectured by experts on the subjects, and is divided in three parts. The first part of the school is devoted to introduce the students to the tools needed from the geometry of smooth manifolds and their relation to mechanics.

This research school features lectures of the world-leading experts that have driven recent developments on structure and geometry in matrix analysis and computations. The participants of the school will benefit from being trained at the forefront of research on structured matrix and geometry-based algorithms, empowering them to make contributions to the state-of-the-art. Structure is central to matrix computations. lt often reflects properties of the underlying application, such as symmetries, and redundancy introduced during linearization or discretization processes.

Analyse numérique & optimisation, contrôle et problèmes inverses a pour objectif de contribuer au développement de l’analyse mathématique et numérique d’équations différentielles et d’équations aux dérivées partielles pour résoudre des problèmes inverses, des problèmes de contrôle et d’optimisation. Ce volet des mathématiques est en plein essor dans la région du Maghreb (en particulier : Algérie, Maroc et Tunisie) et possède un large champ d’applications : industrie (détection pétrolière, usure d’équipement, etc), médecine (cancérologie,etc), épidémiologie, écologie.

The concept of a group is central to essentially all of modern mathematics. In number theory and geometry where groups take central stage in various shapes such as symmetry groups, Galois groups, fundamental groups, reflection groups and permutation groups, the conceptual unification that it provides is most strikingly illustrated. In this school, we present groups and the natural objects they act on in a variety of arithmetic and geometric contexts. Special emphasis will be given to concrete examples, and practical and computational aspects of groups and their actions will be stressed.

The research school will provide a useful background to understand several of the very active research subjects in the wide area of functional analysis. This includes Riesz spaces and Stochastics processes, function theory, differential operators, operator theory on various and natural Banach spaces, some notions of geometry of Banach spaces, semigroup theory and its links with applications, without omitting an introduction to harmonic analysis.

Numeration is an active and developing field of study that encompasses different areas of mathematics and theoretical computer science. The goal of the research school is to introduce graduate students and young researchers to the fundamentals of the geometric, combinatorial, and dynamical aspects of numeration systems as well as to topics of current research. The basic courses of the research school will include lectures on beta expansions, canonical number systems, formal languages, substitutions, and others.