DG-MP-PDE Seminar: The Inverse Calderon Problem for Schoedinger Operator on Riemann Surfaces

We show that on a smooth compact Riemann surface with boundary (M_0, g) the Dirichlet-to-Neumann map of the Schr\"odinger operator \Delta_g + V determines uniquely the potential V. This seemingly analytical problem turns out to have connections with ideas in symplectic geometry and differential topology. We will discuss how these geometrical features arise and the techniques we use to treat them.

This is joint work with Colin Guillarmou of CNRS Nice.

The speaker is partially supported by NSF Grant No. DMS-0807502 during this work.