Calderón problem for a fractional conductivity equation

The classical Calderón problem for the conductivity equation asks if the conductivity of a medium can be determined uniquely by making current and voltage measurements on its boundary. We present an analogous question in the fractional context, called the inverse fractional conductivity problem. Likewise its classical counterpart, the inverse fractional conductivity problem has a rather rich mathematical theory. The study of unique continuation properties is central in the analysis of such inverse problems. We discuss recent progress in inverse problems for the fractional conductivity and other elliptic nonlocal operators.