English

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:

1. Topology of function spaces.
2. Categories and Modules.
3. Algebraic Topology from a Homotopical Viewpoint.
4. The ∞-Categorical Point of View of Thom Spectra.
5. Homological Techniques applied to Modules.
6. Topology of singular spaces with focus on curves and surfaces.

Les langues officielles de l'école sont l'anglais et l'espagnol. Les cours d'introduction seront dispensés en espagnol, et les autres en anglais.

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.

Official language of the school: English. All the main activities and mini-courses will be given in English. Some contributed talks and posters given by students from the region will be in Spanish.

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 school will offer a solid introduction to this rich topic  by presenting the fundamentals of the topology and geometry of singularities of spaces and maps, and of the geometric bifurcation theory, together with the necessary algebraic and analytic tools, aiming to a bunch of current research lines.
Will be presented ongoing research topics such as determinantal varieties, bifurcation of families, fibrations structures and new classes of singularities, Lipschitz geometry of singularities, vision and other applications. All courses will be planned to provide the students with practical tools via the open source computer algebra system ‘Singular’.

Lien vers la cérémonie d'ouverture: https://www.youtube.com/channel/UCth-gA-OAsNYl5wNVjgegPQ

Langue officielle de l'école : anglais

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.

Langues officielles de l'école : anglais

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. A special stress will be on pedagogical aspect, and there will be exercise sessions for the students.

The target audience will consist essentially of young researchers and PhD students from India, deve- loping countries and other countries, who work in this direction or who plan to pursue their research in related areas. Special attention will be given to promote female students.

Langue officielle de l'école : anglais

The school aims to introduce graduate students and young re- searchers to the new trends in Hamiltonian systems and celestial mechanics. To this end, the school is articulated in five highly topical themes in the area, all sharing to a greater or lesser extent the classical N–body problem as a prototypical and paradigmatic case.

Langue officielle de l'école : anglais

The school aims to introduce graduate students and young researchers to key topics in algebraic number theory and arithmetic geometry and their computational aspects. Modular forms and elliptic curves will be central, with a view towards Galois representations, complex multiplication and class field theory. Understanding of the abstract theory will be facilitated by an explicit and algorithmic approach, through an interactive approach where we will make use of freely available computer algebra systems. The participants will be provided with an introduction to the basic material that before proceeding to the more advanced topics.

Langue officielle de l'école : anglais

The study of geometric objects via groupoids appears in many branches of mathematics and physics.

Lie groupoids are an efficient tool in the analytic treatment of singular spaces in order to get a pseudodifferential calculus and index theory. In the context of quantization problems, the symplectic groupoid of a Poisson manifold witnesses very important developments in symplectic geometry in the broad sense. In these contexts lies the question of associating a suitable groupoid with a geometric situation. This is related to the problem of integrating (Lie) algebroids into (Lie or fiberwise Lie) groupoids. Parallel to this, complex manifolds endowed with holomorphic geometric structures are important models in theoretical physics. Their geometric features are interesting from many mathematical points of view.

This school will bring together mathematicians working on various aspects of groupoids in relation with foliations, singular spaces and their applications in order to offer a broad panorama of the techniques and problems encountered.

Langue officielle de l'école : anglais

In this school, we intend to introduce modern mathematical modelling tools which are useful to solve and analyse ecological, medical and environmental challenges. Our aim is to prepare students and staff members for concrete problems arising in mathematical modelling in ecosystems, more particularly environmental and ecological issues that can be applied in the context of South-East Asia. We will present theoretical and numerical lectures about deterministic and stochastic differential equations and their calibration. Practical sessions of free scientific computing software using Freefem++ will be also provided.

Langue officielle de l'école : anglais