Scientific program for 2013
Gunther Uhlmann is spending a few weeks in Paris on February and March 2013 as a laureate of FSMP's Research Chair. Here is the scientific program of his stay.
1) A Minicourse at IHP (11 rue Pierre et Marie Curie 75005 Paris) on Geometry and Inverse Problems
- Tuesday February 5: 10h30-12h in room 314,
- Friday February 8: 10h30-12h Amphithéâtre Hermite,
- Tuesday February 19: 10h30-12h in room 314,
- Tuesday February 26: 10h30-12h in room 314
- Thursday March 7: 10h30-12h in room 314.
Abstract: 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.
Clic here to download the course notes.
2) A minicourse at IHP on Cloaking and Transformation Optics in a workshop organized by the SMF to be held at IHP on Feb 20-22.
More information can be found in:
3) Talk at Journees thematiques de Cergy on "Inverse Problems" on Monday, Feb 4.
Title: Cloaking: Science Meets Science Fiction
Abstract: 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.
More information is at:
4) Seminar at the Laboratoire Jacques Louis Lions at Jussieu on Friday, Feb 8 at 14:00PM.
Title: Travel Time Tomography and Boundary Rigidity
Abstract: 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) Seminar at IHES/X, Feb 19.
Title: On Calderon's Inverse Problem
Abstract: 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.
6) Colloquium. U Grenoble, Feb 15. Same title and abstract as in 3).
A meeting on inverse problems will be organized after the colloquium.
More information is at: