Argentina

L’école de recherche CIMPA "Méthodes Homologiques, Théorie des Représentations et Algèbres Amassées" est destinée aux étudiants doctoraux et postdoctoraux d’Argentine et des pays avoisinants d’Amérique du Sud, et plus spécialement aux étudiants de la région de Mar del Plata. Cette école de recherche est conçue comme une suite de celle intitulée "Méthodes Homologiques et Représentations d’Algèbres Non Commutatives" et du colloque "South-American Meeting on Representations of Algebras and Related Topics" qui se sont tenus tous deux à Mar del Plata en 2006 et 2010.

Le but de cette école est de promouvoir en Amérique du Sud et en particulier dans la région élargie de Salta l’étude des systèmes dynamiques définies sur des ensembles de Cantor. Parmis eux, les sous-décalages, les dynamiques de Bratteli- Vershik, les automates cellulaires, les dynamique de pavages ou les dynamiques sur les entiers p-adiques.

Point processes are well studied objects in probability theory, with applications in many different disciplines such as nuclear physics, materials science, telecommunications, astronomy, artificial intelligence (machine learning) and economics, among others. Some interesting point processes can be obtained as eigenvalues of random matrices or as zeros of series expansions with random coefficients.

One of the goals of this school is to provide latin-american students with the possibility to attend courses and lectures related to Harmonic Analysis and Geometric Measure Theory, and their applications. This school will focus on those aspects of Harmonic Analysis which recently have had a huge impact, in particular in image and signal processing. A characteristic feature is that several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis and Geometric Measure Theory.

The aim of the school is to introduce the participants to the main aspects of the theory of quantum groups (Hopf algebras) and their applications in theoretical physics and mathematics.

Stochastic models are present in many areas of theoretical and applied sciences. The interplay with other areas has been a rich source of challenges and inspiration for probabilists. The present school will have courses on (a) the limiting behavior of rescaled microscopic systems giving rise to macroscopic laws in Physics, (b) on the rescaling of random graphs appearing in Field Theory, and (c) on folding-unfolding transition in Biology.

The area of the school is number theory, broadly understood - analytic, algebraic, combinatorial, with links to groups and geometry.

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.

The school will address a selection of topics of importance in modern research in combinatorics, representation theory, higher structures via the prism of geometry, and their interrelation. Specific themes to be covered are geometric representation theory, quantum groups, the use of higher structures to study the geometry of various spaces, categorification, combinatorial aspects of geometry and cluster algebras.

Langue officielle de l'école : anglais