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SUMMARY:Generalised Radon Transforms - Sean Holman (University of Manchest
 er)
DTSTART:20230131T161500Z
DTEND:20230131T170000Z
UID:TALK194512@talks.cam.ac.uk
DESCRIPTION:Transforms mapping a function to its integrals over a collecti
 on of smooth surfaces are ubiquitous in tomography. In the case that the s
 urfaces are flat with codimension 1\, this is known as the Radon transform
  and the inversion is classical with many well-known applications. When th
 e hypersurfaces are allowed to be curved we obtain a generalised Radon tra
 nsform\; such transforms appear in geophysics and radar. Generalised Radon
  transforms correspond to a double fibration of a larger space and this co
 ncept leads to analytic results including the well-known Bolker condition 
 for microlocal invertibility. In this talk\, I will review the double fibr
 ation framework\, discuss the Bolker condition in a number of specific cas
 es where it holds and fails\, and discuss invertibility of certain transfo
 rms in the spirit of Palamodov.
LOCATION:Seminar Room 1\, Newton Institute
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