A Quarter of Inverse Problems

A new thematic quarter dedicated to inverse problems has just begun at the IHP

By Abby Tabor | Science Journalist at MyScienceWork

Every year, at the Institut Henri Poincaré in Paris, three innovative, multidisciplinary programmes are chosen for the IHP’s thematic quarters. The goal of these quarters is to develop, over a three-month period, extensive reflection around an advanced research topic in mathematics or theoretical physics. From now until July 10th, researchers from around the world will gather to delve into the same subject together: inverse problems. Read on to learn more about the IHP's quarters, as well as the many facets and real-world applications of inverse problems.

 

Every year, at the Institut Henri Poincaré in Paris, three innovative, multidisciplinary programmes are chosen for the IHP’s thematic quarters. The goal of these quarters is to develop, over a three-month period, extensive reflection around an advanced research topic in mathematics or theoretical physics.

The themes addressed during these quarters range from theoretical mathematics to nearly experimental physics, to applied (or practical!) mathematics that could lead to industrial applications: in a word, the whole spectrum of mathematical sciences.

On average, a thematic quarter welcomes about 100 participants (professors, researchers and students, French and foreign) and comprises symposia, classes (possibly at PhD level) and seminars.

Currently Underway: A Quarter of Inverse Problems

A new quarter has just begun, dedicated to inverse problems. These are concerned with the recovery of some unknown quantities involved in a system from the knowledge of specific measurements. Typical examples are:

  • - the boundary distance rigidity problem where one would like to recover the metric tensor of a compact Riemannian manifold with boundary from the knowledge of the geodesic distance between boundary points,
  • - spectral inverse problems where one tries to recover a compact Riemannian manifold from the scattering matrix or from the Dirichlet data of eigenfunctions,
  • - Calderón's inverse conductivity problem where one is interested in recovering the coefficient of a partial differential equation from Cauchy data, and
  • - inverse tomography where one is concerned with inverting integral transformation such as the X-ray or the Radon transforms.


This philosophy of thinking is quite natural in engineering and physical sciences where one aims to determine physical quantities from experimental measurements. It is therefore not surprising that the field of inverse problems bears a lot of applications to other scientific domains, for instance medical imaging, seismography, oil prospection, radar imaging, etc. It also involves a wide spectrum of mathematical fields, such as harmonic analysis, partial differential equations (PDEs), microlocal analysis, Riemannian geometry, spectral theory, probability etc., up to numerical implementations on the more applied side.

To learn more about the program on inverse problems and the thematic quarters in general, to find relevant research or connect with the participants, visit https://ihp.mysciencework.com/.

 

Scientific committee of the program

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

 

This text was adapted and reposted from:

http://iecl.univ-lorraine.fr/~David.Dos-Santos-Ferreira/ipscient.html

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