2021

The goal of this CIMPA research school is twofold. First of all, the school offers a rigorous introduction to the theoretical bases of optimization and optimal control.

The aim of this CIMPA school will be to familiarise graduate students and young researchers with the field of  enumerative and analytic combinatorics,  and to show its many connections to other areas,  especially computer science.  The courses  range from introductory to  more advanced levels.

One of the fascinating bridges between  classical  mechanics  and quantum physics  is expressed  in the fact that the length spectrum  and the Laplace  spectrum  of a closed Riemannian  manifold determine  each other (at least generically). The main goal of this school  is to introduce  graduate  students  and young  researchers to basic facts on these two spectra, and to the above correspondence.

The school aims at introducing graduate students and young researchers to the mathematic of climate science. Lectures will cover key topics in the field focusing on their mathematical complexity and dimension. Climate science is genuinely interdisciplinary and this is reflected in the breath of topics offered in the school: predictability, data assimilation, climate prediction, climate sensitivity and thermodynamics.

The main theme of the proposed school are graph algebras, which are objects of growing interest that lie at the boundary between algebra and analysis among other mathematical fields. Despite being introduced only about a decade ago, Leavitt path algebras, as algebraic counterpart of graph C ∗ -algebras, have arisen in a variety of different contexts as diverse as symbolic dynamics, noncommutative geometry, representation theory, and number theory.

The CIMPA school « Structures ordonnées et leurs applications en finance » claims to be multidisciplinary, while fostering constructive and positive interactions between the different fields that will be covered by the occurrence. Thus, this school is based upon two main lines of action, namely, Mathematical Finance and Stochastic Calculus. However, the look at these topics will be given from an "Order" point of view, that is, within the framework of Algebraic and Analytic Ordered Structures.

Cette école CIMPA est dédiée aux groupoïdes de Lie et aux algébroïdes de Lie. Ces deux notions sont omniprésentes en géométrie et topologie différentielles, elles généralisent respectivement les groupes de Lie et les algèbres de Lie. Certains cours auront pour but l'étude de quelques classes remarquables des groupoïdes de Lie : groupoïdes de contact, groupoïdes symplectiques, groupoïdes de Poisson. D'autres seront consacrés aux algébroïdes de Lie riemanniens, et aux groupoïdes d'ordre supérieur.

The school will provide an introduction to both basic and more advanced topics in the moderntheory of dynamical system and ergodic theory. It will be aimed mostly at Masters level students and thus assume a reasonable general mathematical background but no previous specialised knowledge in the topics covered in the courses. The scientific content of the various courses will be tightly coordinated in order to provide the students with the possibility of a real concrete learning experience which can become the foundation for further study.

This school aims at providing interested graduate students from Uzbekistan and other Central Asian countries with the basic notions and some recent ideas and techniques at an advanced stage of current research in a wide spectrum of themes from classical complex analysis, pluripotential theory, geometry of compact complex manifolds and holomorphic dynamics.

The objective of this research school is to present a wide range of applications of the theory of finite-dimensional optimal control to engineering. First, we will pro­ pose a rigorous introduction to the theoretical basis of the theory with two courses (by F. Chittaro and L. Poggiolini) of Optimal Control completed with exercise sessions. Then, we will propose sev­ eral courses devoted to some applications of the previous courses to some problems in engeneering. The first course (by E.