The Fractional Anisotropic Calderón Problem

The fractional anisotropic Calderón problem asks if we can determine a compact connected Riemannian manifold simply from knowing the metric and the local source-to-solution map for the fractional Laplacian on a given open set. This is a nonlocal analogue of the anisotropic Calderón problem, which has been solved in two dimensions but remains wide open in higher dimensions. In this talk, we will compare these two problems and present a result of Feizmohammadi, Ghosh, Krupchyk, and Uhlmann that solves the fractional problem in dimensions two and higher.