BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Quadratic closed $G_2$-structures Ball, Gavin


I will talk about a special class of closed $G_2$-structures, those satisfying the `quadratic' condition. This is a second order PDE system first written down by Bryant that can be interpreted as a condition on the Ricci curvature of the induced metric, that includes the extremally Ricci-pinched (ERP) condition as a special case. I will talk about various constructions of quadratic closed $G_2$-structures, including the first examples of ERP closed $G_2$-structures that are not locally homogeneous and the first examples of quadratic closed $G_2$-structures that are not ERP. I will discuss the relationship with the Laplace flow, and give new examples of Laplace solitons.

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