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Generalized geometry and pluriclosed flow

Abstract

This dissertation will show the ways in which generalized geometry elucidates the study of pluriclosed flow. In their 2009 paper, Streets and Tian introduce pluriclosed flow -- a parabolic flow of pluriclosed metrics -- and classify some static solutions. In 2018, Streets expanded this into a geometrization conjecture for compact, complex surfaces. The author is able to use these tools to show an equivalence between pluriclosed flow and a non-linear, coupled Hermitian-Yang-Mills type flow. From there, the author is able to more geometrically prove a result of Streets and Warren -- an Evans-Krylov theorem for pluriclosed flow. The author is also able to use this equivalence to prove long-time existence and convergence of the flow on Bismut-flat manifolds and surfaces of non-negative Kodaira dimension.

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