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SUMMARY:Gaussian beams and geometric aspects of Inverse problems - Kachalo
 v\, A (University of Bath)
DTSTART:20111129T140000Z
DTEND:20111129T150000Z
UID:TALK34768@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Geometry plays an important role in inverse problems. For exam
 ple\, reconstruction of second order elliptic selfadjoint differential ope
 rator on the manifold through the gauge transformation can be reduced to t
 he reconstruction of Shrodinger operator\, corresponding to Beltrami-Lapla
 ce operator\, i.e. topology of the manifold \, riemannian metric on it and
  potential. The difficulties mostly related to geometric aspects of the pr
 oblem. If we consider applied invere problems\, we also see\, that the mai
 n problems lies in geometry. For example\, in the main problem of geophysi
 cs - the so called migration problem\, it is necessary to reconstruct high
  frequency wave fields in the media with complicated geometry with many ca
 ustics of different structure.  The difficulties of reconstruction of wave
  fields close to caustics are also of geometric character. To solve the ge
 ometric problems it is necessary to have instruments closely related to th
 e geometry of corresponding problem. One of such instruments is Gaussian b
 eams solutions. In the talk the geometric properties of these solutions an
 d their use in direct and inverse problems will be shown. The problems wit
 h more complicated Finsler geometry will also be discussed.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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