Spectral Problems in Inverse Scattering Theory - 21st IMAGINE OneWorld SIAM-IS Seminar

Explore the intricacies of inverse scattering theory in this 69-minute virtual seminar presented by Fioralba Cakoni from Rutgers University. Delve into the fundamental properties of scattering operators, focusing on scattering poles, non-scattering frequencies, and transmission eigenvalues. Learn how real transmission eigenvalues can be determined from scattering data and what they reveal about material properties of scattering media. Discover a novel approach to modifying scattering data to obtain new spectral problems associated with modified scattering operators, aimed at expanding the applicability of the eigenvalue method to inverse problems for absorbing and dispersive media. The talk covers topics such as qualitative methods, eigenvalues in scattering theory, computation of real transmission eigenvalues, and includes a numerical example involving anisotropic media.

Intro
Scattering by an inhomogeneous Media
Qualitative Methods
Eigenvalues in Scattering Theory
Scattering Poles
Transmission Eigenvalues in General
Determination of Real Transmission Eigenvalues
Computation of Real Transmission Eigenvalues
Numerical Example: Anisotropic Media
Cons of Using Transmission Eigenvalues
Modified scattering operator
Literature