Anisotropic Calderon’s inverse problem asks if the data given by voltageto-current measurements on the boundary of a conducting domain can be used to uniquely determine the anisotropic conductivity in the interior of the domain. Geometric reformulated, this problem becomes: given a compact Riemannian manifold (M, g) with boundary, does the full knowledge of the Dirichlet-to-Neumann map (corresponding to the metric Laplacian −∆g) determine the Riemannian metric g up to isometries fixing the boundary? In this talk, I will explain a positive answer at high frequencies, that is we will show that the D-t-N map of −∆g − λ^2 for λ fixed large enough determines the lens data, i.e. the exit points and directions of incoming geodesics (scattering data), together with travel times; under favourable geometric assumptions, this is known to determine g up to isometries. Joint work with K. Krupchyk, S.K. Sahoo, and G. Uhlmann.
