The non-Abelian X-ray transform

Abstract: I will discuss the problem of how to reconstruct a matrix-valued potential from the knowledge of its scattering data along geodesics on a compact non-trapping Riemannian manifold with boundary.

The problem arises in new experiments designed to measure magnetic fields inside materials by shooting them with neutron beams from different directions, like in a CT scan.

Towards the end of the lecture I will focus on the recent solutionof the injectivity question on simple surfaces for any matrix Lie group.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine