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SUMMARY:Scattering for the Dirichlet-to-Neumann map on singular domains - 
 Ruoyu Wang (Yale University)
DTSTART:20260113T153000Z
DTEND:20260113T163000Z
UID:TALK238171@talks.cam.ac.uk
DESCRIPTION:The DtN map naturally arises in physics\, for example\, in the
  studies of electrostatics and water waves. Heuristically\, it sends the v
 oltage measured at the boundary of a crystal to the density of current flo
 wing through. In this talk\, we discuss a new scattering theory for the Dt
 N map on asymptotically conic domains with Lipschitz boundaries in any dim
 ension\, where the nonlocality of the DtN map has a non-trivial interactio
 n with the singularity of the boundary. We then use the new scattering the
 ory to fully identify the spectrum of the DtN map on 2D polygons with piec
 ewise smooth boundaries\, as an improvement to earlier work of Levitin&nda
 sh\;Parnovski&ndash\;Polterovich&ndash\;Sher. This is joint work with Jeff
  Galkowski and Marcello Malagutti.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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