Title: Some inverse source and coefficient problems for the wave operators (special colloquium)

Date: 10/04/2018

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Inverse problems seek to infer causal factor from the resulting observation, and waves are among the most prevalent and significant observations in nature. In this talk, we will discuss two inverse problems for the acoustic wave equation and its generalizations. The first is an inverse source problem where one attempts to determine an instantaneous source from the boundary Dirichlet data. We give sharp conditions on unique and stable determination, and derive an explicit reconstruction formula for the source. The second is an inverse coefficient problem on a cylinder-like Lorentzian manifold (M,g) for the Lorentzian wave operator perturbed by a vector field A and a function q. We show that local knowledge of the Dirichlet-to-Neumann map (DN-map) stably determines the jets of (g,A,q) up to gauge transformations, and global knowledge of the DN-map stably determines the lens relation of g as well as the light ray transforms of A and q. This is based on joint work with P. Stefanov.