2022

The school aims to introduce graduate students and young researchers to the recent connections between p-adic analysis (understood in a large sense) with mathematical physics and computer science. The courses will be focused on active research areas. The tentative list of courses include: (1) introduction to p-adic analysis; (2) introduction to local zeta functions; (3) p-adic models in quantum physics; (4) the p-adic theory of automata; (5) p-adic electrostatics; (6)  Strings amplitudes, local zeta functions, and log-Coulomb gases.

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:

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.

The school aims to introduce graduate students and young researchers to probabilistic and statistical models, including deterministic models focused on applications in environment and epidemiology. It is also aimed at non-specialist practitioners wishing to connect their research to the field of random modeling. The participants will be provided with an introduction to basic material and necessary background before proceeding with the more advanced topics. Beside lectures, we are also planning sessions devoted to solving exercices and computers experiments.

The central topic of the school is the mutual interaction of algebra, combinatorics and geometry. Objects of research in algebraic geometry are affine as well as projective varieties and their associated invariants which can be studied using methods from algebra and combinatorics. Toric and tropical varieties are instances where such kind of approaches were and still are very successful. In discrete geometry cones, graphs, hyperplane arrangements and matroids are examples of research subjects which naturally play prominent roles in algebra and discrete mathematics.

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

Geometric group theory is a relatively new line of research on its own, inspired by pioneering works of M. Dehn, G.D. Mostow and M. Gromov. It is mainly devoted to the study of countable groups by exploring connections between algebraic properties of such groups and geometric properties of spaces on which these groups act, such as the deck transformation group of a Riemannian manifold. Geometric group theory is a very broad area, and this program aims at introducing young students to different aspects of the theory.

Graph Theory lies on the interface between combinatorics and discrete mathematics. The domain has expanded considerably over the last decades with interactions invarious fields such as the study of social networks, algorithms, computer science, interprobabilities, discrete geometry, producing some spectacular results.

Although cryptography has a long history, it has developed during the 20th century into a modern science with the help of computer science and mathematical objects coming from algebra, number theory, geometry, combinatorics,...