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## Blake Keeler (UNC Chapel Hill), GMA & Visions Seminar

Title: Fluid-Construction of the Hadamard Parametrix for the Wave Operator on a Riemannian Manifold Abstract: A common object of interest in the study of PDEs is the fundamental solution of a differential operator. A fundamental solution allows one to invert the differential operator in question. In Euclidean space one can explicitly construct fundamental solutions for the wave operator, but on a general Riemannian manifold the wave operator has variable coefficients, and it is therefore much more difficult to construct a true fundamental solution.…

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