M17: Spectral Problems in Inverse Scattering Theory for Inhomogeneous Media

Recent progress on spectral properties of certain operators associated with scattering phenomena provided new methods of recovering qualitative information about the unknown inhomogeneity. Spectral properties especially for eigenvalues of specific operators can have applications in a variety of inverse problems in target identification and nondestructive testing. Two well-known examples of such spectral values are transmission eigenvalues and scattering poles. Transmission eigenvalues play an important role in so-called sampling methods; real transmission eigenvalues exist, can be determined from scattering data and provide estimates for the constitutive properties of the scattering object. From a different prospective, the scattering poles that lie at the foundation of scattering theory have applications especially in Schrödinger type formulations of inverse scattering problem. Other perspectives including the design of new appropriate eigenvalue pde problems in connection with the inverse scattering problems will be discussed. Special concern will also be given to the applicability of the proposed methods and the corresponding numerical implementations.

The minisymposium will provide the opportunity to experienced and young researchers to share knowledge and exchange ideas about future directions of research concerning spectral problems in inverse scattering theory. Beyond the applicative aspects, these problems have also their own mathematical interest and beauty in connection with direct and inverse spectral analysis of non-self-adjoint problems.

Organizers:
F. Cakoni, Rutgers University, USA, This email address is being protected from spambots. You need JavaScript enabled to view it.
D. Gintides, National Technical University of Athens, Greece, This email address is being protected from spambots. You need JavaScript enabled to view it.
H. Haddar, INRIA and Ecole Polytechnique , France, This email address is being protected from spambots. You need JavaScript enabled to view it.

Invited Speakers (in alphabetical order):
Lucas Chesnel, Inria/Ecole Polytechnique, France, This email address is being protected from spambots. You need JavaScript enabled to view it.
A new complex spectrum related to invisibiliy in waveguides

Andreas Kleefeld, Forschungszentrum Jülich GmbH, Germany, This email address is being protected from spambots. You need JavaScript enabled to view it.
Improvement of the inside-outside duality method

Audibert Lorenzo, École Polytechnique, France, This email address is being protected from spambots. You need JavaScript enabled to view it.
Transmission eigenvalues with artificial background and their determination from scattering data

Shixu Meng, University of Michigan, USA, This email address is being protected from spambots. You need JavaScript enabled to view it.
Spectral analysis of the modified interior transmission eigenvalue problem in inverse scattering

Peter Monk, University of Delaware, USA, This email address is being protected from spambots. You need JavaScript enabled to view it.
Eigenvalues in inverse scattering

Lukas Pieronek, Forschungszentrum Jülich GmbH, Germany, This email address is being protected from spambots. You need JavaScript enabled to view it.
The method of fundamental solutions for computing interior transmission eigenvalues