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Title:
Multi-valued harmonic functions
Speaker:
Abstract:
Multi-valued functions, with branch points, are familiar in complex analysis. We discuss an extension of the notion to general Riemannian manifolds and a deformation problem involving the asymptotics of the function and the branch set. We will take some time to explain motivations for this question from various topical areas in differential geometry, including "collapsed limits" of Riemannian manifolds with exceptional holonomy and special Lagrangian submanifolds. In the last part of the talk we will explain how Nash-Moser theory can be applied to the deformation problem.
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