Mikhail Belishev: C*-algebras in dynamical inverse problems on manifolds

A reconstruction problem is to recover a Riemannian manifold M via its dynamical or spectral boundary inverse data. The talk is devoted to an algebraic version of the boundary control method (BC-method, Belishev' 1986). By this version, information about the manifold is extracted from the spectrum of a relevant C*-algebra determined by the inverse data. It is the so-called eikonal algebra E(M), which is a subalgebra of the bounded operator algebra. There are three kinds of problems, which are distinguished by the properties of this algebra.