*Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.*

Monday, January 29, 2018

2:10 p.m.

BA6183

PhD Candidate: Ali Feizmohammadi

Co-Supervisors: Spyros Alexakis, Adrian Nachman

Thesis title: Unique Reconstruction of a Potential from the Dirichlet to Neumann Map in Locally CTA Geometries

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Abstract:

Let $(M^3,g)$ be a compact smooth Riemannian manifold with smooth boundary and suppose that $U$ is an open set in $M$ such that $g|_U$ is Euclidean. Let $\Gamma= U \cap \partial M$ be connected and suppose that $U$ is the convex hull of $\Gamma$. We will study the uniqueness of an unknown potential for the Schr\”{o}dinger operator $ -\triangle_g + q $ from the associated Dirichlet to Neumann map, $\Lambda_q$. Indeed, we will prove that if the potential $q$ is a priori explicitly known in $U^c$ then one can uniquely reconstruct $q$ from $\Lambda_q$. We will also give a reconstruction algorithm for the potential. More generally we will also discuss the cases where $\Gamma$ is not connected or $g|_U$ is conformally transversally anisotropic and derive the analogous result.

A copy of the thesis can be found here: Ali Feiz’s Dissertation

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