2019

Since a couple of decades, Finsler geometry has been a very active field of research, with a particular stress on the use of purely metric methods in the investigation of various Finsler metrics that appear naturally in geometry, topology and convexity theory.

The Escuela Latinoamericana de Geometría Algebraica (ELGA) series of schools quickly became a major event for algebraic geometry in Latin America working as meeting point for the whole community due in part to the novelty of having some of the best researchers in our eld lecturing in Latin Americaf

The classical results and open problems that lie at the interface between commutative algebra and algebraic geometry, have undergone a striking evolution over the last quarter of a century, aided in large part by computer algebra calculations. At the heart of all these developments is the concept of syzygies: the analysis of the algebraic relations (syzygies) between the equations defining a geometric object leads to deep insights of its geometric properties.

For more than forty years, string theory has been able to impact in the development of several fields of mathematics. K- theory, algebraic and differential geometry, topology, infinite dimensional analysis, representation theory and derived categories, to mention a few, have been profoundly influenced by “stringy” ideas such as mirror symmetry, conformal field theory, D-branes and quantum cohomology. The main goal of this CIMPA Research School is to provide an introduction to many of these mathematical subjects as well as some background on string theory.

The school is organized around two thematic axes: Hopf algebras and tensor categories. The school is intended to introduce Ph.D. students and young researchers on both areas, to explain how they are interrelated, and also to present applications and new lines of research.

The courses on Hopf algebras aim to present the basics of this theory, the most relevant techniques and the classification program of finite-dimensional Hopf algebras. The theory of Nichols algebras will be presented, and how it fits into the classification program.

Le projet d’École de recherche «Approches algorithmiques et statistiques de l'Apprentissage» est au con uent de l'algorithmique, de l'apprentissage et des statistiques. Notre projet s'inscrit ainsi dans la thématique « Sciences des Données » qui concerne le traitement et l'exploitation de grandes masses d'informations qui peuvent être à la fois hétérogènes, complexes, bruitées, incomplètes et distribuées.

L'objectif de cette école est une initiation à la modélisation mathématique et numérique de la gestion des déchets urbains, allant de leur transport à l'impact sur la nappe. La biodégradation et les phénomènes d'écoulement et de transport (Lixiviat et biogaz) sont les "moteurs" essentiels dans la gestion des centres de stockage. Le recyclage de la phase liquide des déchets ménagers est un autre aspect de cette gestion.

This school aims to offer an intensive teaching session to graduate students and young researchers. That concerns key topics in Algebraic Geometry and Number Theory. Indeed many classical results and methods in these areas are used in flourishing domains of applied mathematics. We selected the following six courses:

The aim of this school is to provide courses for graduate students and young researchers. These courses will focus on Control Theory (and, in particular, Geometric Control and Control of Partial Differential Equations) and also Information Theory. In addition, applications of Control and Information Theory as well as their interactions with other fields such as Economy and Physics will be studied. The scientific contents of the school can be decomposed in two parts. The first part is made of 3 courses (of 6 hours each) in Information Theory and one course in Geometric Control.

Representation theory is a central branch of modern mathematics that studies realizations of abstract non-linear structures using classical linear and/or combinatorial concrete structures like matrices, linear operators and quivers. It is a very active and dynamic area, both heavily influenced by important applications to algebra, combinatorics, geometry, topology, analysis, category theory, number theory, mathematical physics and other branches of mathematics and physics.