ANR Programme BLANC EDITION 2009
Geometric Control Methods, Sub-Riemannian Geometry and Applications

Partners Members Postdoc: Marco Caponigro, from february 2010.

Objectives: Several fundamental problems stemming from robotics, vision and quantum physics can efficiently be modeled in the framework of Geometric Control. The study and analysis of these problems can then be ranked as research questions of sub-Riemannian geometry (SRG for short).
The purpose of this project consists in gathering French mathematicians working on these issues and to create a research network on sub-Riemannian geometry. We also hope, via postdoc positions and conferences, to disseminate the knowledge acquired world-wide, and to stimulate young mathematicians to work in this interdisciplinary area.

Abstract: We plan to address problems involving both ODEs and PDEs, for which geometric control techniques open new horizons. More precisely we plan to study: The approach we are proposing to tackle these scientific challenges is based on techniques developed in the framework of sub-Riemannian geometry and geometric control theory, partially by the members of the team themselves.

Keywords: Geometric control theory, Sub-Riemannian geometry, Carnot Caratheodory distance, Conjugate points, Cut locus, Controllability of the bilinear Schroedinger equation, Hypoelliptic heat equation, Quantum Control.