SÉMINAIRE DE GÉOMÉTRIE SOUS-RIEMANNIENNE - INSTITUT HENRI POINCARÉ, PARIS - 2016/17

The "séminaire de géométrie sous-riemannienne" is a periodic seminar held in Paris since 2011, whose aim is to help connections between the different communities working in sub-Riemannian geometry from different viewpoints. 

The seminar takes place at the Institut Henri Poincaré, 11, rue Pierre et Marie Curie, Paris.
Also during 2016/17, it is hosted as a part of the activities of the ANR project SRGI - Sub-Riemannian Geometry and Interactions

  • Frequence: October 2016 - June 2017, one session per month.
  • Topics: sub-Riemannian geometry, hypoelliptic operators and related fields.
  • Organizers: Davide Barilari, Pierre Pansu.
  • Fall 2016 : 19 Oct - 16 Nov - 14 Dec (confirmed)
  • Spring 2017 : Jan 25 - Feb 22 - Mar 22 - Apr 19 - May 17 - Jun 21 (confirmed)
  • Some notes of the seminars of the past years are available on this blog.
  • The room of the seminar has changed with respect to last year!


********************* NEXT SEMINARS *********************


Wednesday, June 21, 2017 - Salle 201 IHP

  • 15.00 - 16.00 Matthieu Léautaud (CMLS - Ecole polytechnique) - Estimées d'effet tunnel et contrôlabilité approchée pour les équations hypoelliptiques.

    Abstract: Dans cet exposé, on s'intéressera aux propriétés de prolongement unique pour des opérateurs hypoelliptiques de type "sommes de carrés de champs de vecteurs". On donnera tout d'abord une estimée a priori concernant la localisation des fonctions propres. On s'intéressera ensuite aux équations de la chaleur et des ondes associées, pour lesquelles on donnera différentes propriétés de prolongement unique quantitatif. On en déduira le coût de la contrôlabilité approchée pour ces équations, c'est à dire, la taille d'un contrôle qui, agissant localement, peut amener l'état dans un epsilon voisinage d'une cible fixée. On discutera enfin l'optimalité de ces résultats sur une famille d'opérateurs de Grushin. Il s'agit un travail en collaboration avec Camille Laurent.


********************* PAST SEMINARS *********************


Wednesday, October 19, 2016. - Salle 201 IHP

  • 15.00 - 16.00 Francesco Boarotto (CMAP, Ecole Polytechnique) - On the existence of smooth points for the value function of a class of affine optimal control problems

    Abstract: We prove that the value function associated with an affine optimal control problem with quadratic cost plus a potential is smooth on an open and dense subset of the interior of its attainable set. The result is obtained by a careful analysis of points of continuity of the value function, without assuming any condition on singular minimizers. Joint work with Davide Barilari.

Wednesday, November 16, 2016. - Salle 314 IHP

  • 15.00 - 16.00 Andrei Agrachev (SISSA) - Switchings in time-optimal problem for affine systems.
    Abstract: Click here

  • 16.00 - 17.00 Yuri Sachkov (University of Pereslav) - Sub-Riemannian minimizers, cut loci and spheres.

    Abstract: The talk will touch the following themes: - left-invariant sub-Riemannian (SR) structures on Lie groups, - a symmetry method for describing SR minimizers, - examples of studied left-invariant SR geometries (3D Lie groups, Engel group, Cartan group), - limitations of existing methods (Liouville non-integrability of flat SR structures of step > 3 and step 3, rank > 2), - applications of SR geometry to rolling bodies, cars with trailers, and image processing.

Wednesday, December 14, 2016. - Salle 01 IHP

  • 15.00 - 16.00 Valentina Franceschi (CMAP, Ecole Polytechnique) - Isoperimetric inequalities in Carnot-Carathéodory spaces.

    Abstract: The aim of this seminar is to present some results about isoperimetric inequalities in Carnot-Carathéodory spaces connected with the Heisenberg geometry. The Heisenberg group is the framework of an open problem about the shape of isoperimetric sets, known as Pansu’s conjecture. We start by studying the isoperimetric problem in Grushin spaces and Heisenberg type groups, under a symmetry assumption that depends on the dimension. We emphasize a relation between the perimeter in these two types of structure. We conclude by presenting some recent results about constant mean curvature surfaces (hence about isoperimetric sets) in the Riemannian Heisenberg group, focusing our attention on the subriemannian limit.


Wednesday, January 25, 2017 - Salle 201 IHP

  • 15.00 - 16.00 Alexandr Medvedev (SISSA, Trieste) - Constant curvature models in sub-Riemanian geometry.

    Abstract: I present a relatively new approch to equivalence problem in sub-Remannian geometry. We use ideas from parabolic geometries to compute local invariants of sub-Remannian metrics. The problem is algebraic in nature and is related to computation of some special Lie algebra cohomology. As useful illustration I'll show how to classify constant curvature models with a given infinitesimal sub-Riemannian symbol using free step-2 distributions as an example.

  • 16.00 - 17.00 Ivan Beschastnyi (SISSA, Trieste) - Sub-Riemannian Engel models

    Abstract: Abnormal geodesics in Sub-Riemannian geometry have been extensively studied and many interesting results were obtained, but many natural questions still remain to be open. For example, there are only a few results on the singularities of the sphere in a neighbourhood of an abnormal geodesic. One of the problems is that there are no simple models. All the known examples with strictly abnormal geodesics have non-integrable geodesic flows and thus there are no explicit expressions. We give some particular examples of sub-Riemannian structures admitting strict or non-strict abnormal geodesics with integrable geodesic equations. All these models are left-invariant Engel manifolds. We isolate some particularly nice cases that are integrable in terms of elliptic functions and elliptic integrals. Moreover we give a general overview of these structures: we construct normal frames, give a complete classification of left-invariant Engel manifolds that finishes the previous work of A. Almeida, and present optimality results for abnormal geodesics in terms of the invariants of the sub-Riemannian structure. (This is a joint work with Alexandr Medvedev.)


Wednesday, February 22, 2017 - Salle 201 IHP

  • 15.00 - 16.00 Ludovic Sacchelli (CMAP, Ecole Polytechnique) - Sub-Riemannian conjugate loci for contact distributions.

    Abstract: In this talk we present recent results on the geometry of the sub-Riemannian conjugate locus of contact manifolds. We first introduce a general approach to the problem of asymptotics for the exponential map near its starting point, and use it to go beyond the well known 3d case. Since in dimension higher than 3 there may be no natural unique way extend the distribution, this problem also relates to the question of finding intrinsic directions that are transverse to the distribution. We will try to underline some key distinctions between the canonical 3d example and other higher dimensional contact distributions in order to explain the differences in their shape.



Wednesday, March 22, 2017. - Salle 201 IHP

  • 15.00 - 16.30 Yves Colin de Verdière (Institut Fourier, Grenoble) - Les asymptotiques de Weyl pour des laplaciens sous-Riemanniens.
    Abstract: Click here


Wednesday, April 19, 2017 - Salle 201 IHP

  • 15.00 - 16.00 Luca Rizzi (Institut Fourier, Grenoble) - Sub-Riemannian geometric inequalities.

    Abstract: We discuss interpolation inequalities for ideal sub-Riemannian structures (i.e. with no non-trivial abnormal minimizers). As a byproduct, we characterize the sub-Riemannian cut locus as the set of points where the squared sub-Riemannian distance fails to be semiconvex. Specifying our results to the case of the Heisenberg groups, we recover in an intrinsic way the inequalities recently obtained by Balogh, Kristály and Sipos. Moreover, we obtain new results on the measure contraction properties of the standard Grushin structure. The techniques are based on optimal transport and sub-Riemannian Jacobi fields. [Joint work with Davide Barilari]


Wednesday, May 17, 2017 - Salle 201 IHP

  • 15.00 - 16.00 Ismael Bailleul (Univ. Rennes) - Ponts de diffusions sous-elliptiques.

    Abstract: On décrira dans cet exposé le comportement statistique des fluctations d'un pont de diffusion sous-elliptique, conditionné à voyager en un temps court entre deux points non conjugués. Un processus gaussien apparaît dans un échelle naturelle, dont la structure met en jeu la variation seconde de la fonctionnelle d'énergie, dont on donne une formulation nouvelle.



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