The relevance of mathematical analysis to understand and improve the behavior of systems has been steadily increasing in the last years. This relevance is enhanced by the development of scientific computing, that makes it possible not only to analyze, describe and predict the behavior of the systems, but also to optimize it.

We are interested in systems appearing in physics, biology, chemistry, engineering, ... Mathematics provides deep insight in three main applications: to provide qualitative understanding, quantitative simulation, and to optimize the behavior of these systems. We intend to cover these three aspects in this program.

Within this perspective, this program furnishes basic research training in approximation, optimization, qualitative analysis and numerical simulation, which are understood as the main tools for mathematical analysis of systems. It is structured in five Research Units:

Unit 1: Constructive approximation and special functions: theory and applications.
Unit 2: Modeling, numerical analysis and scientific computing: development of mathematical tools for the effective solution of recent problems in Physics and Engineering.
Unit 3: Control of systems governed by differential equations and applications to Physics, Biology, Engineering and other Sciences.
Unit 4: Mathematical programming. Theory, algorithms and applications.
Unit 5: Bifurcation analysis of dynamical systems. Theory, numerics and applications in mathematical modeling.

Each Research Unit is composed of a course, individual research projects and several research seminars. The course is intended to provide the basic aspects of the subject with a broad perspective. The research project focuses on up-to-date subjects, is developed individually and advised by a specific senior researcher. The conferences are taught by high-level researchers, and deal with emerging subjects related to each research unit.