First International Summer School on

Geometry, Mechanics and Control

Castro Urdiales (CIEM), June 25-29,  2007

The International Summer School on Geometry, Mechanics and Control is oriented to Ph.D. students and t postdoctoral students with undergraduate studies in Mathematics, Physics or Engineering, in particular to those who want to begin its research in geometrical aspects of mechanics, numerical integration, field theory and control theory. In this sense, the courses could be a complement to Ph.D. programs of different Universities. The main pretension is to form and attract young researchers of contrasted quality in the International context in leader topics around Mechanics, Differential Geometry and Control.

The School is also open to professionals who want to attend advanced and specialized courses oriented to geometrical techniques in those fields. It  pretends to show an updated version of the knowledge of some basic problems in these topics and to present to the participants  open problems and, in particular,  the applications by means of specialized courses taught by the best international researchers in the respective fields.

The specific scientific profile of the School in 2007 is based on the research lines of Numerical Analysis (in particular, numerical integration), Geometric Mechanics and Control Theory with applications to Engineering, Robotics and Physics.

In 2007, the School will develop two research lines which will linked along the course.  In each of the lines, it will be proposed discussion sessions and presentation of open problems and research to be done in the future.

• Numerical integration and Geometric Mechanics

During the last decade, a remarkable effort has been made in the construction of geometric integrators for Lagrangian and Hamiltonian systems. The main idea consists in looking for numerical methods which preserve one or more geometric invariants associated to those systems (energy, first integrals, symplecticity ...).

• Optimal Control Theory: Applications to Engineering

The mathematical theory of control is a broad area which, from a mathematical point of view, deals with three fundamental problems in Control Theory: modelling, analysis and design. For that, it is used different areas of Mathematics, for instance: Differential and Symplectic Geometry, Stability Theory of Dynamical Systems, Complex Analysis, Differential Analysis, Functional Analysis, Complexity Theory, etc. As it is expected, this approach implies the appearance of new problems in all those areas which suppose a fruitful interaction between them.