2022

Although cryptography has a long history, it has developed during the 20th century into a modern science with the help of computer science and mathematical objects coming from algebra, number theory, geometry, combinatorics,...

Graph Theory lies on the interface between combinatorics and discrete mathematics. The domain has expanded considerably over the last decades with interactions invarious fields such as the study of social networks, algorithms, computer science, interprobabilities, discrete geometry, producing some spectacular results.

The central topic of the school is the mutual interaction of algebra, combinatorics and geometry. Objects of research in algebraic geometry are affine as well as projective varieties and their associated invariants which can be studied using methods from algebra and combinatorics. Toric and tropical varieties are instances where such kind of approaches were and still are very successful. In discrete geometry cones, graphs, hyperplane arrangements and matroids are examples of research subjects which naturally play prominent roles in algebra and discrete mathematics.

The school will focus on interplay between dynamics and algebra, introducing participants to key subjects in the study of these interactions: Groupoid convolution algebras and tensor categories. The techniques developed will be applied to Leavitt path algebras, which encode combinatorics and dynamics of graphs.

Langue officielle de l'école : anglais

The goal of this School is to provide students from Central America and neighboring countries with some elements of the methods and techniques of Algebra applied to Topology.

There will be 6 courses of introductory and advanced levels, and 3 talks. The titles of the courses are:

Combinatorics is at the center of a variety of areas in pure and applied mathematics. In recent years problems arising in algebra and geometry have been better understood and in many cases fully solved by exploiting their relation to certain combinatorial structures. At this school, we aim to introduce the participants to modern geometric techniques that have been used to solve long-standing conjectures in combinatorics and other areas.

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.

The objective of the school is to provide graduate students and young researchers with introductory courses and specialized lectures on partial differential equations (PDE), calculus of variations, and their applications. The courses will concern the contemporary methods as well as recent advances and tools in PDE theory and calculus of variations with various applications in transport theory, shape optimization, kinetic theory, geometric analysis, control theory and engineering. The total duration of the school scientific activities is fifty seven (57) hours.

The theory of surfaces of finite or infinite types, with their geometric structures, with moduli spaces of geometric structures and with some related dynamical systems on these moduli spaces, constitutes some of the most important aspects of low-dimensional topology, geometry and dynamics. In this school, we propose a set of coordinated courses that will concentrate on several aspects of this field and which will give the students the opportunity, at the same time, to learn the basic aspects of these topics, and to have access to important research problems.

Le progrès en mathématiques et l’évolution des outils informatiques ont permis de développer des méthodes numériques capables d’apporter quelques réponses à des problèmes environnementaux, comme la production d’énergies renouvelables, la valorisation des déchets ménagers, la dépollution des eaux usées et son exploitation dans l’agriculture. La modélisation de ces phénomènes, vus du point de vue biologique, offre aux mathématiciens et aux numériciens des problèmes ouverts.