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Research talks;Geometry
A sub-Riemannian distance is obtained when minimizing lengths of paths which are tangent to a distribution of planes. Such distances differ substantially from Riemannian distances, even in the simplest example, the 3-dimensional Heisenberg group. This raises many questions in metric geometry: embeddability in Banach spaces, bi-Lipschitz or bi-Hölder comparison of various examples. Emphasis will be put on Gromov's results on the Hölder homeomorphism problem, and on a quasisymmetric version of it motivated by Riemannian geometry.
A sub-Riemannian distance is obtained when minimizing lengths of paths which are tangent to a distribution of planes. Such distances differ substantially from Riemannian distances, even in the simplest example, the 3-dimensional Heisenberg group. This raises many questions in metric geometry: embeddability in Banach spaces, bi-Lipschitz or bi-Hölder comparison of various examples. Emphasis will be put on Gromov's results on the Hölder ...
53C20 ; 53C15
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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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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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- 261 p.
ISBN 978-3-540-20306-3
Mathématiques & applications , 0043
Localisation : Collection 1er étage
théorie du contrôle # méthode géométrique # variété de dimension 2 # synthèse optimale # système feedback # singularité # projection # contrôle en temps minimal
49J15 ; 49N35
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- viii; 299 p.
ISBN 978-3-03719-163-7
EMS series of lectures in mathematics
Localisation : Ouvrage RdC (GEOM)
géométrie sous-Riemanienne # opérateur hypoelliptique # contrainte non-holonome # contrôle optimal # chemin rugueux
53C17 ; 35H10 ; 60H30 ; 49J15 ; 53-06 ; 00B15
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- vi; 324 p.
ISBN 978-3-03719-162-0
EMS series of lectures in mathematics
Localisation : Ouvrage RdC (GEOM)
géométrie sous-Riemanienne # opérateur hypoelliptique # contrainte non-holonome # contrôle optimal # chemin rugueux
53C17 ; 35H10 ; 60H30 ; 49J15 ; 53-06 ; 00B15
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