Microlocal analysis/inverse problems/PSDOs
Connections for Women: Microlocal Analysis August 29, 2019 - August 30, 2019
Location: SLMath: Eisenbud Auditorium
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
I will motivate a quick introduction to pseudo-differential operators by discussing the so-called Calderon's problem, that is, whether knowledge of the Dirichlet-to-Neumann map (or the Neumann-to-Dirichlet map) at the boundary determines the conductivity of a body in the interior. This problem has applications in Electric Impedance Tomography (EIT). I will in particular discuss uniqueness at the boundary, interior uniqueness using Complex Geometrical Optics (CGO solutions), and if time permits, layer stripping reconstruction algorithms in the case of isotropic conductivities.