Argentina

The CIMPA research school "Homological Methods, Representation Theory and Cluster Algebras" is intended for PhD and postdoctoral students from Argentina and surrounding South American countries and specifically for students in the region of Mar del Plata.

The goal of this school is to promote in South America, and more specifically in a large region around Salta, the study of dynamical systems defined on Cantor sets.

Among them, the subshifts, the Bratteli-Vershik dynamics, the cellular automata, the tiling dynamics or those on the set of p-adic integers. Many point of views will be investigated : ergodic theory, topological dynamics, theoretical computer science, discrete geometry, number theory, numeration systems, automata theory, …

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.

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.

Official language of the school: English