SÉMINAIRE DE GÉOMÉTRIE SOUS-RIEMANNIENNE - INSTITUT HENRI POINCARÉ, PARIS - 2017/18

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

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OTHER INFORMATIONS

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 2017 - June 2018, one session per month.
- Topics: sub-Riemannian geometry, hypoelliptic operators and related fields.
- Organizers: Davide Barilari, Pierre Pansu.
- Fall 2017 : Oct 4 - Nov 8 - Dec 6 (red text = canceled)
- Spring 2018 : Jan 17 - Feb 14 - Mar 14 - Apr 11 - May 23 - Jun 20
- Some notes of the seminars of the past years are available on this blog.
- The
**room**of the seminars are either**01**(ground floor) or**201**(2nd floor), please check!

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*NEXT SEMINARS*

*Wednesday, December 6, 2017. - Salle 01 IHP*

- 15.00 - 16.00
**Alexey Remizov**(CNRS, CMAP, Ecole Polytechnique) -*Singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics*

Abstract: We present a series of recent results about singularities of geodesic flows on 2-dimensional surfaces with smooth signature varying metric (such metrics are often called pseudo-Riemannian). Generically, a surface with a pseudo-Riemannian metric contains a curve that consists of points where the metric degenerates. These points are singular points of the geodesic flow generated by this metric. The behavior of geodesics at degenerate points differs from those in Riemannian metrics. For instance, geodesics cannot pass through a degenerate point in arbitrary tangent directions, but only in certain directions said to be admissible. (It is worst observing that the same phenomenon appears in singular metrics of different types, for instance, in almost-Riemannian structures.) The number of admissible directions for generic pseudo-Riemannian metrics at almost all degenerate points is 1 or 3 (at some isolated points it could be 2). The main technical tool for this study is the theory of local normal forms for vector fields with non-isolated singular points, a far generalization of the theory started by H. PoincarĂ© and H. Dulac.

*Wednesday, January 17, 2018 - Salle 01 IHP*

- 15.00 - 16.00
**Erlend Grong**(Orsay) -*Sub-Laplacians on forms and cohomology.*

Abstract: For any sub-Riemannian structure, there is a unique corresponding second order operator on functions which is symmetric with respect to some given volume form. We will call this operator the sub-Laplacian. We discuss the challenges, results and applications that comes from attempting to generalize this operator to differential forms. We will mainly be concerned with operators which has a WeitzenbĂ¶ck decomposition, that is, can be constructed from the Hessian of an affine connection and a zero order differential operator. As one applications, we get results related to cohomology of totally geodesic foliations.

*Wednesday, February 14, 2018 - Salle 314 IHP*

- 15.00 - 16.00
**Davide Barilari**(Paris Diderot) -*What is sub-Riemannian scalar curvature? A result and some open questions**Abstract:*In this talk I will discuss some possible approaches to define a notion of scalar curvature in sub-Riemannian geometry. A natural one is to try to extract this invariant from the asymptotics of the volume of small balls, similarly to what happens in Riemannian geometry. In the sub-Riemannian setting this computation is not trivial for different reasons: balls are not smooth and not geodesically homogeneous, geodesics are parametrized on a non-compact set, the cut locus from a point is adjacent to the point itself etc. We will compute this asymptotics in the 3D contact case, and then discuss some difficulties arising when trying to consider higher dimensional situations. [Joint work with A. Lerario and I. Beschastnyi]

*Wednesday, March 14, 2018. - Salle 01 IHP*

- 15.00 - 16.30
**TBA**(-) -*TBA*

*Abstract:*TBA

*Wednesday, April 11, 2018 - Salle 201 IHP*

- 15.00 - 16.00
**TBA**(-) -*TBA.*

*Abstract:*TBA

*Wednesday, May 23, 2018 - Salle 201 IHP*

- 15.00 - 16.00
**Antonio Lerario**(SISSA) -*TBA*

*Abstract:*TBA

*Wednesday, June 20, 2018 - Salle 201 IHP*

- 15.00 - 16.00
**TBA**(-) -*TBA*

*Abstract:*TBA

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*PAST SEMINARS*

*Wednesday, October 4, 2017. - Salle 201 IHP*

- 15.00 - 16.00
**Dario Prandi**(L2S, Supelec) -*Quantum confinement and spectral theory of (sub-)Laplacians*

*Abstract:*

OTHER INFORMATIONS

- Links to the wepage of the last years:

Séminaire de Géométrie sous-riemannienne - 2016/2017

Séminaire de Géométrie sous-riemannienne - 2015/2016

Séminaire de Géométrie sous-riemannienne - 2014/2015

Séminaire de Géométrie sous-riemannienne - 2013/2014

Séminaire de Géométrie sous-riemannienne - 2012/2013

Séminaire de Géométrie sous-riemannienne - 2011/2012 - (organized by Enrico Le Donne) - Blog of the "Geometry and Control" seminar in SISSA