2013

The CIMPA research school "Partial Differential Equations in Mechanics" will focus on certain recent progress of mathematical analysis and numerical computations related to the partial differential equations namely to fluid mechanics for engineering science. Lectures aim to introduce advanced techniques for the numerical computation of solutions of several classes of PDEs. In particular finite element, finite difference and spectral methods, definition of numerical simulations for different models, comparison with the predictions of analytic results will be presented.

The development of Computational methods for partial differential equations (PDEs) is a key tool for the development of science and technology. For its development, it is important to have a deep understanding of the classical and new methodologies used in numerical methods. The summer school will provide an overview of some techniques that allow one to address the computational challenges encountered in different applications.

Mathematical modelling in biology and analysis of the resulting equations
are a main challanging scientific problem. This domain interests an increasing
mathematical community in the world as well as biologists, doctors, engineers
in environmental science for their possible applications. The various recent PDE
methods and the last most significant progress in this domain need to be exchanged
and developed with Cuba and other countries of the Caribbean area.
The school aims at presenting some of the current approaches in PDE modelling

The primary aim of this research school is to give an introduction to the theory of graphs, codes, and designs with the major focus on the relationship between these three areas. For instance how techniques in graph theory and design theory can be used in the construction of error – correcting codes.

The second aim is to provide an introduction to current research topics in graphs, codes, and designs. To this end, sections on more advanced topics are included, and a number of interesting and challenging open problems will be highlighted and discussed in some detail.

During the last three decades and in a technological and economical complex world, mathematical models play an important role in the decision-making tools. Indeed, whether to develop and calibrate models, measure and control risks associated with economic phenomena or financial instruments, mathematical tools provide skills highly appreciated to better understand these phenomena and improve prediction of their inherent risks.

The school aims to introducing undergraduate, master and Ph.D. students from Brazil and other countries in South America, to active topics in Representation Theory, focusing on algebraic and geometric methods. This is a two-weeks long event, where the first week is devoted to the study of algebraic methods arising in Representation Theory, while the second week is concerned with geometric tools applied to Representation Theory. The program for both weeks consists on mini- courses taught by mathematicians from different countries including Argentina, Brazil, Canada, France and Switzerland.

The aim of this school is to introduce graduate students and postdoctoral researchers to contemporary developments in the theory of Associative and Nonassociative Algebras and Dialgebras.

Algebraic geometry is a key area of mathematical research of international significance. The Theory of Moduli Spaces has experienced an extraordinary development in recent decades, finding an increasing number of mathematical connections with other fields of mathematics and physics. This school is an introduction to subjects of current interest related to moduli spaces of augmented bundles and physics.

Differential Galois Theory is a subject of great development in the last years, with important ramifications that cover algebra, analysis, geometry, algorithmic or applied mathematics. It represents a useful technique in order to treat a wide range of problems related with differential equations, mainly linear, many of them of application, for instance, in physics.