Le programme scientifique de 2013
Gunther Uhlmann (université de Washington), lauréat en 2012 de la Chaire d'Excellence de la FSMP, séjourne à ce titre à Paris en février-mars 2013. Voici le programme scientifique de son séjour :
1) Mini-cours à l'IHP (5 rue Pierre et Marie Curie 75005 Paris) sur le thème Geometry and Inverse Problems
- mardi 05/02: 10h30-12h en salle 314,
- vendredi 08/02: 10h30-12h Amphithéâtre Hermite,
- mardi 19/02: 10h30-12h en salle 314,
- mardi 26/02: 10h30-12h en salle 314
- jeudi 07/03: 10h30-12h en salle 314.
Résumé : We will consider several inverse problems that consist on determining the Riemannian metric of a compact Riemannian manifold with boundary from information given at the boundary.
The first problem arises in travel time tomography which consists in determining the index of refraction or sound speed of a medium by making travel time measurements. This problem can be recast as a geometric inverse problem: Can one determine the Riemannian metric of a compact Riemannian manifold with boundary from the distance function between boundary points?
The second problem is Calder\'on's problem. The question is whether one can determine the conductivity of a medium by making voltage and current measurements at the boundary. This problem can be recast also as a geometric problem: Can one determine the Riemannian metric of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map associated to the Laplace-Beltrami operator?
We will survey what is known about these problems, and some connections between them.
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2) Mini-cours à l'IHP sur le thème Cloaking and Transformation Optics dans le cadre d'un workshop organisé par la SMF du 20 au 22 février.
Pour en savoir plus, consultez le site :
http://www.proba.jussieu.fr/pageperso/garnier/SMF/index.html
3) Conférence aux Journées thématiques de Cergy sur le thème des Problèmes inverses le lundi 4 Février
Titre : Cloaking: Science Meets Science Fiction
Résumé: Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last decade or so there have been several scientific proposals to achieve invisibility. We will introduce some of these in a non-technical fashion concentrating on the so-called "transformation optics" that has received the most attention in the scientific literature.
Plus de renseignements ici :
http://www.u-cergy.fr/_attachments/problemes-inverses-actualite/InverseProblems-2013.pdf?download=true
4) Seminaire au Laboratoire Jacques Louis Lions, à Jussieu, vendredi 8 février à 14h.
Titre: Travel Time Tomography and Boundary Rigidity
Résumé : We will survey some recent results on the inverse problem of
determining the index of refraction of a medium by measuring the travel
times of waves going through the medium. This can be recast as a geometric
inverse problem: Can we determine the Riemannian metric of a Riemannian
manifold with boundary from the distance function between boundary points.
This is the boundary rigidity problem. We will also consider the linearized
problem which consists on determining a symmetric two tensor from its
integral along geodesics.
5) Séminaire IHES/X le 19 février
Titre : On Calderon's Inverse Problem
Résumé : We consider the inverse problem proposed by Calderon which
consists on determining the electrical conductivity of a body by
making voltage and current measurements at the boundary. We
concentrate on the case of partial measurements where the
measurements are made on an open subset of the boundary.
Plus d'informations sur cet événement très bientôt.
6) Colloque à l'Université de Grenoble le 15 février
Titre : Cloaking: Science Meets Science Fiction
Résumé: Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last decade or so there have been several scientific proposals to achieve invisibility. We will introduce some of these in a non-technical fashion concentrating on the so-called "transformation optics" that has received the most attention in the scientific literature.
A meeting on inverse problems will be organized after the colloquium.
Plus d'informations sur :
https://mail.google.com/mail/?shva=1#search/bonnetier/13c809159029712f