Leo Tzou: The inverse Calderón problem for Schrödinger operator on Riemann surfaces

Abstract. We show that on a smooth compact Riemann surface with boundary (M_0; g) the Dirichlet-to-Neumann map of the Schrödinger 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. We will also see how geometric concepts such as holonomy groups and cohomology theory are encoded in the Dirichlet-to-Neumann map.

This is joint work with Colin Guillarmou of Ecolé Normale Superiér Paris and Pierre Albin of University of Chicago Urbana Champaign. The speaker is partially supported by NSF Grant No. DMS-0807502 and FInnish Academy Fellowship during this work.