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SUMMARY:Microlocal analysis &amp\; inverse problems - Jan Bohr (University
  of Cambridge)
DTSTART:20200612T110000Z
DTEND:20200612T120000Z
UID:TALK142336@talks.cam.ac.uk
CONTACT:Renato Velozo
DESCRIPTION:After whetting the appetite for some neat geometric inverse pr
 oblems\, the talk is meant to give a gentle introduction to some bits of m
 icrolocal analysis that have been introduced in the inverse problems commu
 nity by Uhlmann and Vasy in 2012 [1]. Since then they have become a key to
 ol in the treatment of local tomography problems\, most notably resolving 
 the boundary rigidity conjecture for a large class of manifolds [2]. We wi
 ll confine ourselves to one of the simplest problems (determining a functi
 on in the Euclidean unit-ball from its line integrals) and explain how so 
 called scattering pseudodifferential operators can be used to prove inject
 ivity results.\n\n[1] Uhlmann\, Vasy: The inverse problem for the local ge
 odesic ray transform. Invent. Math. 205 (2016)\n\n[2] Uhlmann\, Vasy\, Ste
 fanov: Local and global boundary rigidity and the geodesic X-ray transform
  in the normal gauge. arXiv.1702.03638
LOCATION:Online (Ask for the link to rav25@cam.ac.uk).
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