Analysis & Applied Math

The talk is based on OpenAI's announcement of 6 October 2026 on recovering a smooth Riemannian metric from a local Dirichlet-to-Neumann map. Beginning with Calder\'on's original question, we explore a connection with Hartogs' extension phenomenon. Boundary measurements determine a special kernel on a crossed set, satisfying one elliptic equation in each variable. Its extension towards the diagonal provides a route to recovering the metric. We explain the roles of common Hilbert bases, interpolation inequalities, and Carleman estimates in this approach.