"Modelling, Identification, Control, and Design with respect to Shapes and Geometries"

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The theme of this research and training program and its long-term objectives are the study of the mathematical and theoretical aspects of shapes and geometries in the modeling, design, control, and identification of physical and technological systems. Fundamental ideas come from systems theory, optimization, and control theory, but the modeling, optimization, or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. This area of research has an important potential for applications and for responding to challenging and pressing issues in many different areas: optimal design of mechanical parts (automotive and aerospace industry), positioning of sensors and actuators, control of the position of the free boundary in material sciences, active control of noise, image processing, free and moving boundary problems, design of medical devices, design and control of thin structures, control of the drag by small changes in the shape of the wing of an aircraft, optimal swimming, etc... The program concentrates on three intertwined projects of intrinsic interest that have been chosen sufficiently distant to provide a broad platform for the program but are very closely connected by common mathematical tools and methodologies: P1. Courant metrics, velocity generated diffeomorphisms, evolution equations, and geometrical variational principles; P2. Design of drug release dynamics and drug eluting stents; P3. Grid adaptation and identification of Lagrangian Coherent Structures in fluids versus image segmentation.