BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Fioralba Cakoni (Rutgers University) DTSTART:20211007T160000Z DTEND:20211007T170000Z DTSTAMP:20260423T052930Z UID:Inverse/60 DESCRIPTION:Title: Singularities Almost Always Scatter: Regularity Results for Non-scatterin g Inhomogeneities\nby Fioralba Cakoni (Rutgers University) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nA p erplexing question in scattering theory is whether there are incoming tim e harmonic waves\, at particular frequencies\, that are not scattered by a given inhomogeneity\, in other words the inhomogeneity is invisible to pr obing by such waves. We refer to wave numbers\, that correspond to freque ncies for which there exists a non-scattering incoming wave\, as non-scatt ering. This question is inherently related to the solution of inverse scat tering problem for inhomogeneous media. The attempt to provide an answer to this question has led to the so-called transmission eigenvalue problem with the wave number as the eigen-parameter. This is non-selfadjoint eige nvalue problem with challenging mathematical structure. The non-scattering wave numbers form a subset of real transmission eigenvalues. A positive answer to the existence of non-scattering wave numbers is already known fo r spherical inhomogeneities and a negative answer was given for inhomog eneities with corners. Up to very recently little was known about non-scat tering inhomogeneities that are neither spherical symmetric nor having sup port that contains a corner. In this presentation we discuss some new res ults for general inhomogeneities. More specifically we examine necessary c onditions for an inhomogeneity to be non-scattering\, or equivalently\, by negation\, sufficient conditions for it to be scattering. These condition s are formulated in terms of the regularity of the boundary and refractive index of the inhomogeneity. Our approach makes a connection between non-s cattering configuration and free boundary methods. \n\nThis presentation i s based on a joint work with Michael Vogelius.\n LOCATION:https://researchseminars.org/talk/Inverse/60/ END:VEVENT END:VCALENDAR