Summer Pre-school on Inverse Problems
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.

The  audience  will mainly  consist  in newcomers in the  field, PhD students, postdoctoral fellows, as well as more experienced researchers.   The school ambitions  are to encourage PhD students and postdoctoral fellows to engage their research in this field through the introductory courses and to advertise the current trends  of the field.

Scientific Committee

Victor Guillemin (MIT)
Hiroshi Isozaki (University of Tsukuba)
Gilles Lebeau (Université Nice Sophia-Antipolis)
Gabriel Paternain (University of Cambridge)
Gunther Uhlmann  (University of Washington)
Steve Zelditch (Northwestern University)

Organizing Committee

David Dos Santos Ferreira (Institut Elie Cartan de Lorraine)
Colin Guillarmou (ENS Paris)
Matti Lassas (University of Helsinki)
Jérôme Le Rousseau (Université d’Orléans)


On Inverse Scattering and the Calderón Problem
Lecture 1 –  Lecture 2 –
Link to written notes

On the Geodesic X-ray Transform

On Spectral Rigidity for Analytic Domains
Lecture 1Lecture 2

Survey talks

5 survey talks in addition to the mini courses.

The Boundary Control Method

Reconstruction Methods

Inverse Problems with Partial Data in Dimension Two

The Boundary Rigidity

Cloaking and Invisibility Issues