Boundary control and inverse problems

The talk deals with one approach to Inverse Problems based on their relations to the Boundary Control Theory (the so-called BC-method). To demonstrate the opportunities of the approach we choose, perhaps, the most impressive of its achievements: that is a reconstruction of Riemannian manifolds via boundary spectral or dynamical data. In the spectral statement the inverse problem is to recover a manifold via given spectrum of its Laplacian (with Dirichlet boundary data) and boundary traces of normal derivatives of eigenfunctions; dynamical problem is to recover a manifold via its response operator (dynamical Dirichlet-to-Neumann map). The BC-method gives a unified viewpoint on these problems and efficient procedures solving them.