The Calderon Problem and Metric Properties of Electrical Networks

The inverse problem in the theory of electrical networks, also known as the discrete Calderón problem, consists of reconstructing an electrical network from its response matrix. In some practical applications, it becomes necessary to reconstruct the network from its effective resistance matrix, which can be considered as the pseudo-inverse of a response matrix. In our talk, we consider this problem from the perspective of metric geometry and provide a sketch of an explicit method for its solution using the theory of positive Grassmannians.