2021

A complex number is called algebraic if it is a root of a non-constant polynomial with integer coefficients and is transcendental otherwise. Over recent decades, the transcendental nature of special values of certain arithmetic functions which verify functional equations has been a fascinating branch of Number Theory and attracts an incredible number of work. However, beautiful mysteries remain unsolved.

The school will focus on some stochastic aspects of mathematics and on algorithms used in this context. More precisely, classical random structures such as Markov chains, random walks, discrete combinatorial structures, random texts, chaotic dynamical systems will be considered and some tools to study them, mainly analytic combinatorics, will be given.

Les géométries algébriques réelle et effective ont connu un essor considérable ces dernières années, grâce notamment à l'invention de nouveaux outils et à l'utilisation de méthodes issues d'autres domaines des mathématiques (géométrie algébrique complexe, géométrie tropicale, géométrie symplectique, topologie algébrique, combinatoire, géométrie algorithmique, puissances de calcul actuelles sans pareil …).

L’objectif de cette Ecole de Recherche est de présenter différents aspects de l’analyse mathématique d’équations aux dérivées partielles et de leur résolution numérique, en prenant appui sur des exemples issus d’autres secteurs scientifiques (mécanique, physique…). Grâce à cette Ecole de Recherche, de nombreux enseignants-chercheurs et doctorants pourront avoir accès aux résultats récents des recherches menées sur ces thématiques pertinentes, notamment du point de vue des applications.

CIMPA-2020 is addressed for researchers and students (postgraduate/undergraduate) to acquire a training in the field of mathematics applied to medicine. A wide class of mathematical models and applications in issues related to tumor growth, population dynamics, pattern formation and their implications in developmental cancer biology will be developed.

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.

CIMPA-2020 is addressed for researchers and students (postgraduate/undergraduate) to acquire a training in the field of mathematics applied to medicine. A wide class of mathematical models and applications in issues related to tumor growth, population dynamics, pattern formation and their implications in developmental cancer biology will be developed.

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 aim of this school is to promote the development of mathematics in Madagascar, especially in the area of non-associative algebra, providing new research opportunities for the professors and post-graduate students from the University of Antananarivo and other Malagasy universities.

Topics of school include Non-associative algebras, Deformations, Lie algebras, Leibniz algebras and Computational Methods.

Official language of the school: English

This School aims to bring together graduate students and young researchers from all  regions in Brazil and countries of the South America as audience, and confirmed researchers from all over the world representing different approaches to singularities in Mathematics as speakers.