Title: Transmission Eigenvalues in Inverse Scattering Theory 


Abstract: 


The transmission eigenvalue problem is a new class of eigenvalue
problems that has recently appeared in inverse scattering theory for
inhomogeneous media.  
Such eigenvalues provide information about material properties of the
scattering object and can be determined from scattering data, hence
can play an important role in a variety of problems in target
identication.  
The transmission eigenvalue problem is non-linear and non-selfadjoint
which make its mathematical investigation challenging and
interesting. 


In this lecture we will describe how the transmission eigenvalue
problem arises in scattering theory, how transmission eigenvalues can
be computed from scattering data,  
 what is known mathematically about these eigenvalues and what kind of
 information can they provide on the index of refraction of the
 inhomogeneous medium.  
 For the sake of simplicity, most of our mathematical exposition will
 be done for the case of scattering for isotropic media and at the end
 of the lecture we will discuss the interesting case of anisotropic
 media.  
We end our lecture with a list of open problems on transmission
eigenvalues of interest to inverse scattering and thermo-acoustic
imaging.