Inverse problems for real principal type operators

Inverse problems research concentrates on the mathematical theory and practical implementation of indirect measurements. Applications are found in numerous research fields involving scientific, medical or industrial imaging; familiar examples include X-ray computed tomography and ultrasound imaging. Inverse problems have a rich mathematical theory employing modern methods in partial differential equations (PDEs), harmonic analysis, and differential geometry.

In this talk we outline a recent approach to develop general theory for inverse problems for PDEs (real principal type equations in particular). The work presents a unified point of view to inverse boundary value problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.

This is joint work with Lauri Oksanen (UCL), Plamen Stefanov (Purdue) and Gunther Uhlmann (Washington / IAS HKUST).