Inverse Problems and Control Theory “(In)Stability Results for The Light-Ray Transform”

Abstract:  In Lorentzian geometry, the light-ray transform is the operator that integrates functions over lightlike geodesics. It appears naturally in the study of wave equations, geometric scattering rigidity, and inverse problems. In this talk, I will discuss some work in progress with L. Busch and L. Oksanen, about the stability of this operator. First, I will present an instability result: the modulus of continuity cannot be smaller than certain polynomial. This can be upgraded to a logarithmic bound in the Gevrey category. Secondly, on stationary geometries, I will show how to obtain a stability result for moments of order k, using moments of the light-ray transform from 0 to k.

Speaker: Sebastián Muñoz Thon, Université Paris-Saclay