2013

The main topics of the school cover Singularities in Geometry and Topology and their applications. More precisely it includes singularities of maps:singularities of polynomial maps, Jacobian conjecture, Milnor fibrations, and singularities of varieties: singularities of real and complex surfaces, characteristic classes, intersection homology, hyperplane arrangements.

Applications to medical imaging, astrophysics, computer vision or robotic will be original features of the school.

The school is devoted to three classes of problem: the generalized Nash equilibrium problems, the bilevel problems and the Mathematical Programming with Equilibrium Constraints. They interact through their mathematical analysis as well as their applications.

Fourier theory has been a useful analytic tool in studying discrete structures. Some of the areas where this theory has been particulaly fruitful are additive combinatorics, eigen values of graphs and random walks on finite groups or in the study of Boolean functions used in computer sciences.

This school, organized from October 28th till November 9th 2013, focuses on the theme of Lévy and auto-similar processes which is a rapidly growing domain of the probability theory. Due to its various theoretical aspects (potential theory, classic and harmonic analysis, algebra, operator theory) and applications (physics equations, finance, insurances, dynamics of the populations…), this theme attracts numerous mathematicians from different fields.

This ERC aims to deliver to young mathematicians from Senegal and other neighboring countries a triple purpose.

The first objective will focus on state of the art numerical methods (Finite volume, Finite Element, Discontinuous Galerkin) with applications in environmental fluid mechanics. The lectures and tutorial classes via computers will be inspired by the challenges that the West African countries encounters in terms of numerical simulation: sediment transport with applications to rivers ans coastal areas (Senegal river), urban hydrology, pollutant transport etc...

The purpose of this school is to focus on two particularly active areas which are representative of new interactions between harmonic analysis and signal and image processing that had striking developments in the last 10 years:

• Sparse representation and Compressed sensing,
• Multifractal Analysis.

Research and study of hypergeometric functions began from 17th century. Mathematicians like Gauss, Euler and Kummar are pioneers of the theory. Hypergeometric functions are applied in many areas of mathematics including representation theory, mathematical physics and etc. Beginning of the representation theory goes to the late 1800s. It uses many concepts of many branches of modern mathematics. Relationships between representation theory and hypergeometric functions are very tight, for example, coefficients of the representation matrices are usually described by hypergeometric functions.

The theory of algebraic curves over finite fields is a very active subject both from a theoretical and an applied point of view. The research school aims to cover theoretical, computational and applied aspects of the topic and thus will be useful to a broad range of students and young mathematicians interested in algebra and its applications.

For a long time, Combinatorics was considered mainly as recreational mathematics. But in the past few decades, it has emerged as a mainstream area, with rich connections with more classical ones such as algebra, topology, geometry and probability theory. Moreover, because of its close links with computer science, Combinatorics has become a crucial scientific endeavor.

The School is to take place at the African Institute of Mathematical Sciences (which recently signed the MOU with CIMPA) and will be a part of initiatives of the Mathematics for the Planet Earth year.