BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Tanya Christiansen (University of Missouri)
DTSTART:20220324T160000Z
DTEND:20220324T170000Z
DTSTAMP:20260423T035613Z
UID:Inverse/85
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/85/"
 >The semiclassical structure of the scattering matrix for a manifold with 
 infinite cylindrical end</a>\nby Tanya Christiansen (University of Missour
 i) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\
 nAbstract\nWe study the microlocal properties of the scattering\nmatrix as
 sociated to the semiclassical \nSchr\\"odinger operator $P=h^2\\Delta_X+V$
  on a Riemannian\nmanifold with an infinite cylindrical end.  Let $Y$ deno
 te the cross section of the end\, which is not necessarily connected.  We 
 show that under suitable hypotheses\, microlocally  the scattering matrix 
 is a Fourier integral operator associated to the graph of the scattering m
 ap $\\kappa:\\mathcal{D}_{\\kappa}\\to T^*Y$\, with $\\mathcal{D}_\\kappa\
 \subset T^*Y$.  The scattering map\n$\\kappa$ and its domain $\\mathcal{D}
 _\\kappa$ are \ndetermined by the Hamilton flow of the principal symbol of
  $P$.\nAs an application we prove that\, under additional hypotheses on th
 e scattering map\,\nthe eigenvalues of the associated unitary scattering m
 atrix are equidistributed on the unit circle.\n\nThis talk is based on joi
 nt work with A. Uribe.\n
LOCATION:https://researchseminars.org/talk/Inverse/85/
END:VEVENT
END:VCALENDAR