Title: On the stability of Gel'fand's inverse spectral problem

Speaker: Jinpeng LU, University of Helsinki

Time: 9.22, 2025, 14:30-15:30

Location: 2309

Abstract: Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Then I will discuss our recent works on the uniqueness and stability of the inverse problem for certain classes of metric-measure spaces.