April 13 – 17, 2015
Inverse problems are concerned with the recovery of some unknown quan- tities involved in a system from the knowledge of specific measurements. While this philosophy of thinking is quite natural in engineering and physical sciences where one aims to determine physical quantities from experimen- tal measurements, it gives rise to very challenging mathematical questions. Besides, it involves a wide spectrum of mathematical fields, such as har- monic analysis, partial differential equations (PDEs), microlocal analysis, Riemannian geometry, spectral theory, probability etc. up to numerical im- plementations on the more applied side. The field is flourishing. Large groups and very strong schools have emerged. Several breakthroughs were achieved in spectral inverse problems or inverse problems with partial data, and new theoretical inverse problems appeared, induced by applications to physical sciences, for instance in thermoacoustic medical imaging, radar de- tection, or related to invisibility issues.
The field of Inverse Problems is in full expansion as shown by the number of programs organized in recent times in the main mathematical research institutes throughout the world. The Institut Henri Poincar´e will host an international three months program on theoretical inverse problems starting in April-May-June 2015. In connection to this program, an introductory school in this field is organized at CIRM. The school will consist in a few expository talks and three courses:
• a course on inverse scattering and the Calder´on problem;
• a course on spectral rigidity for analytic domains;
• a course on the geodesic X-ray transform.
Victor Guillemin (MIT)
Gunther Uhlmann (University of Washington)
Steve Zelditch (Northwestern University)
David Dos Santos Ferreira (Institut Elie Cartan de Lorraine)
On Inverse Scattering and the Calderón Problem
On the Geodesic X-ray Transform
On Spectral Rigidity for Analytic Domains
5 survey talks in addition to the mini courses.
The Boundary Control Method
Inverse Problems with Partial Data in Dimension Two
The Boundary Rigidity
Cloaking and Invisibility Issues