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Constant mean curvature surfaces: an integrable perspective

4:00 pm Thursday, November 14, 2014
Franz Pedit (UMass-Amherst)

Starting from Hopf's observation that compact genus zero CMC surfaces in 3-space have to be round spheres, we will discuss the contributions integrable system methods have made in understanding compact (and non-compact) CMC surfaces. The basic ingredients will be the self-duality equations over a Riemann surface, its circle worth of deformations, spectral curves, loop algebra valued meromorphic connections, the Riemann-Hilbert problem, and abelianization of flat connections. We will focus on the conceptual ideas and augment them with computer visualization and experiments.

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