This week's seminars
Analysis and/of PDE: Spectral invariants of the Dirichlet-to-Neumann map
20 February 2020 14:00 in CM301
It is a classical problem of inverse spectral geometry to find geometric quantities that can be determined from the spectrum of an elliptic differential operator. For example, it follows from the work of Girouard, Parnovski, Polterovich and Sher that spectral asymptotics for the Dirichlet-to-Neumann map of the Laplacian determine the number and lengths of the boundary components of a surface, but not any more. In this talk, I will explain how we can recover more geometric information from a surface if we consider instead the Dirichlet-to-Neumann maps associated with Schrödinger operators. I will also explain how this has application to the inverse scattering problem, and therefore to non-destructive testing. This is joint work with Simon St-Amant (Université de Montréal).
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