2017

La Théorie des Graphes se situe à l’interface de la combinatoire et des mathématiques discrètes. C’est une thématique en plein essor ces dernières décennies et en évolution constante tant du point de vue recherche que du point de vue applications. dans différents domaines tels que l’étude de réseaux, l’informatique, les probabilités , la biologie .... L’étude de ces graphes a donné lieu à des résultats spectaculaires en combinatoires ces dernières années comme par exemple la résolution du problème des graphes parfaits.

The CIMPA research school "Representation Theory and Applications to Differential Equations" is intended for PhD and postdoctoral students from Jamaica and surrounding Caribbean and American countries and specifically for students in the region. The CIMPA research school “Representation Theory and Applications to Differential Equations" offers courses and research talks on advanced research topics related to the representation theory of groups and algebras, related differential equations and other topics. The school lasts two weeks, featuring 6 courses and 12 research talks.

In this school, we will introduce differential equations as modeling tools in engineering (fluid dynamics, traffic flow) and bio-mathematical applications (coagulation, epidemics). We will discuss analytical properties of differential equations and their numerical solution.

L’objectif de cette Ecole est une initiation aux développements récents de la géométrie complexe multi-variables (avec les concepts de nature analytique qui l’accompagnent : positivité, courants, pluri-sous-harmonicité et opérateurs de Lelong-Poincaré et de Monge-Ampère, etc.) dans diverses directions : la dynamique holomorphe en plusieurs variables complexes, la déformation de structures géométriques complexes en structures «tropicales» (c’est-à-dire relevant de la géométrie attachée au calcul max/plus), la géométrie torique et sa relation avec la géométrie convexe réelle, enfin la transpo

Over the past thirty years there has been a growing need and interest for nonsmooth optimization methods. Nonsmoothness of objective or constraint functions may arise, for example, from heterogeneous material properties, from process controls and safety mechanisms that dynamically switch on and off; from variational inequality representations of free boundaries, phase transitions, contacts with friction; and from numerical schemes such as upwind finite differences and flux limiters.

This school is an introduction to subjects of algebraic coding theory and quasi cyclic codes. The purpose of this school is to introduce young mathematicians and students to the foundations of the the study of error correcting codes by means of algebra over finite rings and finite fields. Powerful decoding algorithms and connections with geometric codes will be emphasized when relevant. Applications to convolutional codes will be presented .

This school is an introduction to subjects of current interest in algebraic geometry, with emphasis on group actions on algebraic varieties. The goal is to train Latin American students and young researchers on the different techniques in transformation groups (algebraic, symplectic, topological, etc.) and to highlight the many interactions between these viewpoints. There will be 5 courses, all of them delivered by well recognized specialists from France, USA and Mexico.

During the Research School the leading mathematicians will present a lot
of lectures in the most important areas of modern algebra such as Jordan
(super)algebras, conformal algebras, Sabinin algebras, composition algebras
and GPI-algebras. There will be conferences about the last investigations
of leading researches in modern algebra. New scientific relations will be
established to produce in future new joint researches.

One of the goals of this school is to provide latin-american students with the possibility to attend courses and lectures related to Harmonic Analysis and Geometric Measure Theory, and their applications. This school will focus on those aspects of Harmonic Analysis which recently have had a huge impact, in particular in image and signal processing. A characteristic feature is that several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis and Geometric Measure Theory.

Research in the solvability of partial differential equations (PDE’s) leads us to a much wider scope. In the realization that alternative methods can be used for proving the existence and uniqueness of solutions of linear and nonlinear PDE’s, a new research area in Applied Mathematics was introduced. The theory of Sobolev spaces was developed, which turned out to be a suitable setting in which to apply ideas of functional analysis to glean information concerning PDE’s.