# Mathematics Colloquia and Seminars

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### Ambient metrics and exceptional holonomy

**PDE and Applied Math Seminar**

Speaker: | Robin Graham, University of Washington, Seattle |

Location: | 1147 MSB |

Start time: | Fri, Mar 13 2015, 4:10PM |

The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of an infinite-dimensional family of metrics in dimension 7 whose holonomy is the split real form of the exceptional group 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.

Reception after talk.