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Home » MLA-Graduate Student Seminar: Noncommutative techniques for inverting the sub-Riemannian X-ray Transform on the Heisenberg Group

Seminar

MLA-Graduate Student Seminar: Noncommutative techniques for inverting the sub-Riemannian X-ray Transform on the Heisenberg Group November 25, 2019 (01:30 PM PST - 02:30 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Steven Flynn (University of California, Santa Cruz)
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We formulate a sub-Riemannian X-ray transform on contact manifolds. Such manifolds are modeled locally (via their Gromov-Hausdorff tangent cones) by 2-step nilpotent Lie groups, with the Heisenberg group exhibiting the simplest nontrivial case. We explicitly describe the Heisenberg ray transform, and an ongoing attempt at its inversion using tools from noncommutative harmonic analysis in the spirit of Helgason that rhyme with the Euclidean case. The primary challenge in this geometry inhibiting standard tools is the ubiquitous presence of conjugate points.

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