Argentina

We intend to introduce the students to some important new developments in Arrangement Theory, Singularity Theory and related areas in Algebraic Geometry. The main emphasis will be the interaction of this two subjects. The school will draw attention on a very active area of research in Mathematics, which is likely to produce major advances in various branches of applied sciences such as computer science (visualization of singular spaces and geometric modeling) or robotics ( configuration spaces of bar mechanisms).

In recent years, an explosive development of algorithms and software constitutes a breakthrough in the field of polynomial system solving, which makes feasible the solution of several problems that had been intractable up to now, and which provides the means necessary for experimentation and conjecture. These algorithms have created a significant interest for effective algebraic geometry and computer algebra among scientists, engineers, and applied mathematicians.

We intend to provide an introduction to various important aspects of Algebraic Geometry, including applications of current interest. The courses during the first week will focus on the following subjects:

The general aim of ELAMs is to strenght the interaction and collaborationg among latinoamerican mathematicians giving the opportunity to meet, share their work and discuss issues concerning mathematics in this region.

The mathematical aim is to contribute to the development of new subjects, making PhD student and young researchers familiar with them.

The objective is to present to the students the state of the art of dynamic optimization with regard to Deterministic and Stochastic Optimal Control. This will be accomplished through several courses about the modeling, the analysis and the numerical resolution of optimal control problems.

This Winter School will cover different topics in Non Commutative Geometry, and its connections with other areas of Mathematics and Physics, such as Operator Index Theory, Strings, Representations, Operator Algebras, and K-Theory.

The purpose of the School is to introduce young Latin-American mathematicians to the most recent developments of Real Analysis. The intention is to cover a range as broad as possible, from theory to applications. Thus, the school will include topics such as Vector Valued Transference Methods, new aspects of Calderon-Zygmund theory, Semigroups of Linear Operators, Heisenberg Nilmanifolds together with the discussion of fluid dynamics problems involving Fractional Powers of the Laplacian, and applications of Harmonic Analysis to Medical Tomography.

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.

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.

By bringing together young researchers (of Argentina and neighboring countries in particular but not only), a central overall objective is to fill an area of vacancy in Argentine mathematics, both at the research and the formation level. While a few well established probability schools are regularly held in Brazil, it remains a challenge to build a strong tradition of probability in Argentina.