Brazil

The main aim of the School is to introduce students and young researchers to the differential-geometric methods of nonlinear control. Basic concepts and results of geometric control theory will be presented: optimal control, nonlinear controllability and observability, systems equivalence, linearization. The proposed mini-courses cover a large part of geometric nonlinear control: from classical results to recent ones and from purely theoretical to applied ones.

The school aims to introducing undergraduate, master and Ph.D. students from Brazil and other countries in South America, to active topics in Representation Theory, focusing on algebraic and geometric methods. This is a two-weeks long event, where the first week is devoted to the study of algebraic methods arising in Representation Theory, while the second week is concerned with geometric tools applied to Representation Theory. The program for both weeks consists on mini- courses taught by mathematicians from different countries including Argentina, Brazil, Canada, France and Switzerland.

This research school intends to present to the participants (mainly Ph.D. students) applications of commutative and non-commutative algebra to coding theory. Thus we will have courses and talks on the following topics (but not limited to them):

Recently, a beautiful convergence of different areas of mathematics has occurred. Developments in fields, such as Free probability, Random Matrices, Rough Paths theory, and numerical methods for (partial/stochastic) differential equations, share common algebro-combinatorial formalisms. Over time it became clear that on the one hand different classes of set partitions related to cumulants and moments, and Hopf and (pre-/post-)Lie algebraic structures on the other hand are central in these advancements.

The goal of this CIMPA research school is to train young mathematicians working in Latin America in some of the most active areas of research in Algebraic Geometry, as well as to promote greater interaction among researchers and students, and to build a network of collaborations.

The first week of the school will consist of 4 mini-courses covering different aspects of Algebraic Geometry. There will be also poster presentations by young researchers and students. The second week will consist of research talks by leading specialists, as well as presentations by young researchers.

La combinatoire joue un rôle fondamental, en tant qu'outil mathématique, dans plusieurs branches des sciences comme l'informatique, les mathématiques appliquées, la biologie, la physique, la chimie etc. Plusieurs problèmes des sciences citées peuvent être exprimés par des modèles combinatoires. Ainsi, l'analyse de ces modèles aboutit souvent à la conception d'algorithmes pour les résoudre. Cette liaison étroite entre la combinatoire et l'algorithmique constituera le cadre général de l'école.

The objective of this school is mainly to spread the knowledge on Parallel and Distributed Algorithms, considering their theoretical and pratical aspects. The activities and discussions will focus on algorithms and applications suitable for intensive parallelization. What characterizes these applications is the possibility to obtain, through the utilization of parallel computers, a solution for larger problems than those currently being solved by sequential computers.

Mathematical Logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Its inception was motivated by the study of foundations of mathematics and it has found applications in many areas, specially in Theoretical Computer Science. The four pillars of Mathematical Logic are Set Theory, Recursion Theory, Model Theory and Proof Theory. This school intends to cover all such subjects, on different levels and with different applications.  The proposed tree basic courses have the great advantage of requiring no or little prior knowledge.

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.