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Yang-Mills Flow on Special Holonomy Manifolds

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Monday, October 15, 2018
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3:15 pm - 4:15 pm
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Alex Waldron (Michigan State University, Mathematics)
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Geometry/topology Seminar

I will describe an upcoming paper with Goncalo Oliveira investigating the properties of Yang-Mills flow on base manifolds with restricted holonomy, generalizing known results from the 4-d and Kahler cases. We show that finite-time blowup is governed by the F^7 component of the curvature in the G_2 and Spin(7) cases, and by the appropriate curvature component in the remaining cases on Berger's list. Assuming that this component remains bounded along the flow, we show that the infinite-time bubbling set is calibrated by the defining (n-4)-form.