Geometry and incompleteness of G2-moduli spaces

G2-manifolds are an exceptional class of Ricci-flat manifolds, whose geometric properties are related to the algebra of octonions. In the compact setting, the deformations of G2-manifolds are known to be parametrised by finite-dimensional moduli spaces which admit a natural analogue of the Weil-Petersson metric, whose properties remain quite mysterious. In this talk, we will explain how to partially understand the geometry of the moduli spaces near certain degenerate limits of G2-manifolds.