Simple Surfaces are Boundary Rigid

The boundary rigidity problem, originating in geophysics in the early 20th century, asks if a compact Riemannian manifold with boundary is determined by knowing the distance between each pair of boundary points. In this talk, we will present a result of Pestov and Uhlmann which shows that this is true for so-called "simple" surfaces and illustrate why the simplicity assumption is important in the proof.