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.

Combinatorics plays an important role as a mathematical tool in diverse fields such as computer science, applied mathematics, operational research, biology, chemistry, etc. Many problems in these sciences can be formulated using combinatorial models. The analysis of these models often yields algorithms to solve such problems. The main aim of the Summer School is to explore this close relationship between combinatorics and algorithms.