Boundary control and tomography of Riemannian manifolds (the BC-method)

The BC-method provides one of the approaches to inverse problems of mathematical physics. A characteristic feature of this method is the great variety of interdisciplinary relations involved: in addition to partial differential equations as a source of problems, use is made of control theory and systems theory, asymptotic methods, functional analysis, operator theory, Banach algebras, and so on. The purpose of this talk is to present the principal ideas and tools of the BC-method and to give a survey of some results. One of the main achievements of the method is chosen for presentation: the reconstruction of Riemannian manifolds from dynamical and spectral boundary data.