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Title:
An application of numerical techniques to rigorous proof in special holonomy
Speaker:
Abstract:
Approximations of Calabi-Yau metric are a popular tool to produce heuristics, but so far have not been leveraged to rigorously prove theorems in geometry. I present one work in progress, in which we prove that the real loci of certain Calabi-Yau manifolds admit harmonic nowhere vanishing 1-forms, which are needed for an application in G2-geometry. I will explain the proof strategy, which consists of two parts: first, I formulate an estimate for the difference between approximate metric and true Calabi-Yau metric in terms of the Ricci curvature of the approximate metric which is of independent interest. Second, I explain the connection between nowhere vanishing 1-forms with respect to the two different metrics. This is joint work with Rodrigo Barbosa, Michael Douglas, and Yidi Qi.
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