Ambient metrics and exceptional holonomy

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Robin Graham, University of Washington
Fine Hall 314

Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of interest in recent years.  This talk will outline a construction of an infinite-dimensional family of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$.  An open dense subset of the family has holonomy equal to $G_2$.  The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.This is work with Travis Willse and generalizes results of Leistner and Nurowski.