2015

The purpose of this school is to introduce young researchers to some of the most important areas of number theory where research is active and also includes applications such as cryptography. In particular, this CIMPA research school presents the state of research on the arithmetic of number fields which interests many researchers in Morocco and neighboring countries.

The main purpose of this school is to give to PhD students and to young researchers of the introductory courses on subjects using at the same time the differential geometry and the non- associative algebras. Besides, the program of this school will contain conferences of researchers specialists in these domains with the aim of showing to the participants some current subjects of researches in the themes of this school.

In this research school topics related to minimal surfaces, overdetermined problems and, more generally, geometric analysis will be studied. The main objective is to present to students and young researchers how tools from differential geometry and analysis of partial differential equations can be combined to obtain interesting, new results in both fields.

This Research School is intended for the study of Partial Differential Equations (PDEs) arising in geometry and physics. The major PDEs classes will be considered (elliptic, parabolic and hyperbolic), both for the construction of particular solutions and the classification of different qualitative behavior scenarios. Through the 6 courses, students will be given the opportunity to know the state of the art of the subject, with an introduction to the most recent techniques.

The main objective of the school is to boost the regional activities in Hamiltonian and Lagrangian Dynamics, with focus on some new research trends. We expect it will contribute to increase the interaction between researchers and students from Argentina, Brasil, Chile, México and Uruguay.

The goal of this Research School is to present various probabilistic models for the spread of infectious diseases, which is clearly one of the major problems that Africa has to face in the coming years.

As Sir Ronald Ross wrote in 1911, « epidemiology must be considered mathematically ». Mathematical epidemiology was first based mainly upon deterministic ODE models, corresponding to the study of well established epidemics in large populations.

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, …

Non-commutative algebraic structures are at the core of recent developments of fundamental mathematics, from quantum groups (Hopf algebras) to non-commutative geometry. In this project of Research School complementary aspects are considered inside this direction: homology and cohomology, Frobenius algebras, representation theory and path algebras as well as Leavitt path algebras. Those subjects as well as their articulations will provide a first strong inside to the theory.

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.

This is a 10-days school of mathematics & theoretical computer science for students from Iran and neighbor countries. It is devoted to mathematical aspects of tilings in the various contexts where they appear, with an effort to achieve coherence of the program: