The starting part for the talk is work of Hitchin, giving a variational description of special geometric structures in dimensions 6, 7, 8 in terms of a volume functional. (See for example “The geometry of 3- forms in six dimensions”, JDG 2000.) In the talk we will discuss some developments of this idea, in the case of 7 dimensions and G2 holonomy. In one direction we will consider boundary value problems, and reductions of the G2 equation to 3 and 4 dimensions. In another direction we will consider adiabatic limits, making contact with the theory of maximal submanifolds in spaces of indefinite signature.
This video is part of Harvard University‘s conference JDG 2017.
