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Objectives

The Intensive Programme for Research (IPR) which is proposed here is based on three axis: Geometry, Mechanics and Control, with an evident interrelationship. We pretend to boost the research in several topics of these fields from different lines of action. The specific topics which we pretend to deal with are detailed in the following heading. Some of them constitute novel research lines and some of the research groups which will participate in this programme wants to incorporate to these lines in order to become an international reference.

We would like to influence, on one hand, in the training of young peopleon emerging research lines, offering a rigorous and deep approach in these topics and approximating them to the applications. On the other hand, it is our purpose to give a larger international visibility to the research of quality made by different Spanish groups, which have made important inputs to different open problems in the topics previously mentioned.

Programme

The Programme will be developed in a continuous way along 2008 in the facilities of ICMAT (Madrid) with timely actions at other Universities. These activities will consist in an opening Workshop on “Geometry, Mechanics and Control”, a Summer School with three advanced courses related to the topics of geometric reduction and its applications and Stochastic Mechanics, and an Iberoamerican Meeting on Geometric Mechanics and Control Theory. Moreover, along 2008, there will be thematic one-day meetings which will deal specific aspects in this area. In addition, there will be research visits of senior and junior researchers at ICMAT.

The topics in which we pretend to emphasize in this IPR are the following:

• Geometric Integration
• Geometric Control
• Quantum computation
• Classical Field Theory
• Geometric Theory of Hamilton Jacobi
• Simmetries and reduction in Mechanics from a geometric perspective and their applications
• Stochastic Mechanics
• Geometry and Integrability of mechanical systems
• Geometry of mechanical systems with constraints

All of them are centered around the applications of different techniques coming from Differential Geometry to problems in Mechanics, Control Theory and Field Theory.

Activities

Visits of researchers at ICMat

• Marin Kobilarov (CalTech, USA)
  From 4 until 20 of December 2008.
• Sebastián José Ferraro (Universidad Nacional del Sur, Argentina)
  From 2 until 19 of December 2008.
• Bronislaw Jakubczyk (Institute of Mathematics, Polish Academy of Sciences, Poland)
  From 2 until 7 of June 2008
• Janusz Grabowski (Institute of Mathematics, Polish Academy of Sciences, Poland)
  From 26 of May until 6 of June 2008
• Edith Padrón and Juan Carlos Marrero (Universidad de La Laguna)
  From 12 until 16 of May 2008.
• Paula Balseiro (Universidad Nacional de la Plata, Argentina)
  From 1 of February until 23 of December 2008.
• María Barbero Liñán (Universidad Politécnica de Cataluña)
  From 31 of March until 13 of April 2008.

Red de Geometría, Mecánica y Control	Ingenio Mathematica	SIMUMAT
Universidad de La Laguna	Universidade de Santiago de Compostela	Universidad de Zaragoza
Consejo Superior de Investigaciones Científicas	Ministerio de Educación y Ciencia