Abstract

After whetting the appetite for some neat geometric inverse problems, the talk is meant to give a gentle introduction to some bits of microlocal analysis that have been introduced in the inverse problems community by Uhlmann and Vasy in 2012 [1]. Since then they have become a key tool in the treatment of local tomography problems, most notably resolving the boundary rigidity conjecture for a large class of manifolds [2]. We will confine ourselves to one of the simplest problems (determining a function in the Euclidean unit-ball from its line integrals) and explain how so called scattering pseudodifferential operators can be used to prove injectivity results.

[1] Uhlmann, Vasy: The inverse problem for the local geodesic ray transform. Invent. Math. 205 (2016)

[2] Uhlmann, Vasy, Stefanov: Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge. arXiv.1702.03638