Niky Kamran (Mc Gill University Montreal) A survey of the Calder\'on inverse problem.

The Calder\'on inverse problem asks if the metric of a smooth compact Riemannian manifold with boundary is uniquely determined from the knowledge of the Dirichlet-to-Neumann map, that is the map that assigns to prescribed boundary data the normal derivative of the corresponding solution of the Laplace-Beltrami equation. While the Calder\'on inverse problem is still open in its full generality, there are a number of results that provide either an affirmative answer or counterexamples, depending on which special assumptions are made about the background geometry. The talk will be an introduction to the Calderon problem and a survey of some of the main uniqueness and non-uniqueness results.