This project addresses questions in the mathematical theory of inverse problems, a research field at the interface between pure and applied mathematics. The techniques that will be developed lie at the intersection of partial differential equations and geometry, with affinity to control theory and general relativity. The so-called Lorentzian Calderon problem is central to the proposal. A physical interpretation of the problem asks us to recover a moving medium given data generated by acoustic waves probing the medium. When the medium is not moving, this problem is well-understood, but it is open in general. The project develops new methods to solve this problem, and considers also related questions that belong in the family of geometric inverse boundary value problems.

2022

2026