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UID:5db43c1b3ee933d9edc4953c749788f7
CATEGORIES:Mathematical Physics Seminar
CREATED:20230831T124808
SUMMARY:Foiralba Cakoni -  Transmission Eigenvalues and Non-Scattering  Inhomogeneities 
DESCRIPTION:<p style="text-align: center; background: #f7f7f7; margin: 0in 0in 7.5pt;">
 <strong>Foiralba Cakoni - Rutgers University</strong></p><p style="text-ali
 gn: center; background: #f7f7f7; orphans: 2; widows: 2; word-spacing: 0px; 
 margin: 0in 0in 7.5pt;"><strong>Date/Time/Location</strong><strong><br> </s
 trong><strong>Thursday, September 14th, 12:00pm; Hill Center 705</strong></
 p><p style="text-align: center; background: #f7f7f7; orphans: 2; widows: 2;
  word-spacing: 0px;">&nbsp;<strong>Transmission Eigenvalues and Non-Scatter
 ing &nbsp;Inhomogeneities&nbsp;</strong></p><p style="text-align: center; b
 ackground: #f7f7f7; orphans: 2; widows: 2; word-spacing: 0px;">Abstract:&nb
 sp;&nbsp;A perplexing question in scattering theory is whether there &nbsp;
 are incoming time harmonic waves, at particular frequencies, that are not s
 cattered by a given inhomogeneity, in other words the inhomogeneity is invi
 sible to probing by such waves. &nbsp;We refer to wave numbers, that corres
 pond to frequencies for which there exists a non-scattering incoming wave, 
 as non-scattering. This question is inherently related to the solution of i
 nverse scattering problem for inhomogeneous media. &nbsp;The attempt to pro
 vide an answer to this question has led to the so-called transmission eigen
 value problem with the wave number as the eigen-parameter. This is &nbsp;no
 n-selfadjoint eigenvalue problem with challenging mathematical structure. T
 he non-scattering wave numbers form a subset of real transmission eigenvalu
 es. &nbsp;Although transmission eigenvalues exists for a large class of inh
 omogeneities, a positive answer to the existence of non-scattering wave num
 bers was already known for spherical inhomogeneities and a negative answer 
 &nbsp;was &nbsp;given for inhomogeneities with corners. Up to very recently
  little was known about non-scattering inhomogeneities that are neither sph
 erical symmetric nor having support that contains a corner. In this present
 ation we discuss &nbsp;some new results in this regard for general inhomoge
 neities including anisotropic media.&nbsp;<br> <br> More precisely, we &nbs
 p;present the state of the art on the spectral theory for the transmission 
 eigenvalue problem. Then we examine necessary conditions for a transmission
  eigenvalue to be non-scattering wave number. These conditions are formulat
 ed in terms of the regularity of the boundary and refractive index of the i
 nhomogeneity, using free boundary methods.&nbsp; This presentation is based
  on joint works with Michael Vogelius and Jingni Xiao.</p>
DTSTAMP:20260907T072112
DTSTART;TZID=America/New_York:20230914T120000
DTEND;TZID=America/New_York:20230914T140000
SEQUENCE:0
TRANSP:OPAQUE
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