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Fractional Dirac operators and Geometric reconstruction

Hadrian Quan
Tuesday, March 29, 2022 - 1:30pm to 3:30pm
PDL C-401

I will report on joint work with Gunther Uhlmann regarding the anisotropic fractional Calderon problem for Dirac operators on closed manifolds. Namely we show that knowledge of the source-to-solution map of the fractional Dirac operator, for data sources supported in an arbitrary open set in a Riemannian manifold allows one to reconstruct the Riemannian manifold, its Clifford module structure, and the associated connection (up to an isometry fixing the initial set). I will begin this talk by introducing this question of recovering global geometric data only from local measurements by considering properties of solutions to the linear wave equation, before later introducing Dirac operators (fractional or not).

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