Yaroslav Kurylev: Gel'fand Inverse Spectral Problem and the Boundary Control Method (lecture 3)

These lectures will be devoted to (mainly) the question of uniqueness in the inverse problem of the recovery of a Riemannian manifold from its boundary or local spectral data, namely, the set of eigenvalues and corresponding eigenfunctions of its Laplacian on the boundary of the manifold or an open set in its interior. The main tool to be explained is the BC-method pioneered by M.Belishev in late 80th. In addition to Laplacian, we will discuss some other type of operators. At the end of the course we will consider the issue of stability in this Gel'fand inverse problem under various geometric assumptions on the class of the manifolds.