BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Steven Flynn (University of Bath) DTSTART:20210402T140000Z DTEND:20210402T150000Z DTSTAMP:20260423T035745Z UID:SRS/12 DESCRIPTION:Title: Unr aveling X-ray Transforms on the Heisenberg group\nby Steven Flynn (Uni versity of Bath) as part of Sub-Riemannian Seminars\n\n\nAbstract\nThe cla ssical X-ray Transform maps a function on Euclidean space to a function o n the space of lines on this Euclidean space by integrating the function o ver the given line. Inverting the X-ray transform has wide-ranging applica tions\, including to medical imaging and seismology. Much work has been do ne to understand this inverse problem in Euclidean space\, Euclidean domai ns\, and more generally\, for symmetric spaces and Riemannian manifolds wi th boundary where the lines become geodesics. We formulate a sub-Riemannia n version of the X-ray transform on the simplest sub-Riemannnian manifold\ , the Heisenberg group. Here serious geometric obstructions to classical i nverse problems\, such as existence of conjugate points\, appear generical ly. With tools adapted to the geometry\, such as an operator-valued Fourie r Slice Theorem\, we prove nonetheless that an integrable function on the Heisenberg group is indeed determined by its line integrals over sub-Riema nnian (as well as over its compatible Riemannian and Lorentzian) geodesics .\n\nWe also pose an abundance of accessible follow-up questions\, standar d in the inverse problems community\, concerning the sub-Riemannian case\, and report progress answering some of them.\n LOCATION:https://researchseminars.org/talk/SRS/12/ END:VEVENT END:VCALENDAR