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Research talks;Control Theory and Optimization;Geometry
This will be an introduction to sub-Riemannian geometry from the point of view of control theory. We will define sub-Riemannian structures and prove the Chow Theorem. We will describe normal and abnormal geodesics and discuss the completeness of the Carnot-Carathéodory distance (Hopf-Rinow Theorem). Several examples will be given (Heisenberg group, Martinet distribution, Grusin plane).
53C17 ; 49Jxx
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Research talks;Probability and Statistics
We discuss hypoelliptic and subelliptic diffusions; the lectures include the following topics: Malliavin calculus; Hormander's theorem; smoothness of transition probabilities under Hormander's brackets condition; control theory and Stroock-Varadhan's support theorems; hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semi-groups; notions of curvature related to sub-Riemannian diffusions.
We discuss hypoelliptic and subelliptic diffusions; the lectures include the following topics: Malliavin calculus; Hormander's theorem; smoothness of transition probabilities under Hormander's brackets condition; control theory and Stroock-Varadhan's support theorems; hypoelliptic heat kernel estimates; gradient estimates and Harnack type inequalities for subelliptic diffusion semi-groups; notions of curvature related to sub-Riemannian ...
60H07 ; 60J60 ; 58J65
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Research talks;Algebraic and Complex Geometry
In this course, we will define the sub-Laplacian associated with a sub-Riemannian structure, and we will describe its hypoellipticity under the Hormander condition. We will introduce the main tools for the study of sub-elliptic PDEs.
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- v; 142 p.
ISBN 978-1-4704-2646-0
Memoirs of the American Mathematical Society , 1225
Localisation : Collection 1er étage
géométrie sous Riemannienne # contrôle de systèmes affines # courbure # courbe de Jacobi
49-02 ; 53C17 ; 49J15 ; 58B20
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