Inverse problem for prototypical nonlocal operators such as the fractional Laplacian display strikingly strong uniqueness, stability and single measurement results. These fundamentally rely on global variants of the unique continuation property for these nonlocal operators and dual flexibility properties in the form of Runge approximation results. In this talk, I introduce these properties and discuss some recent results on the relation between the classical and fractional Calderon problems.

This is based on joint work with G. Covi, T. Ghosh, M. Salo and G. Uhlmann.