Sergey Grigorian

Deformations of $G_{2}$ structures



Abstract

$G_2$ structures on 7-dimensional manifolds arise naturally in supersymmetric M-theory compactifications, in general with fluxes. An important special case is when fluxes are turned off - this gives torsion-free $G_2$ structures, which correspond to manifolds with holonomy $G_2$. Here we review recent results on deformations of $G_2$ structures with torsion, as well as results on the geometry of the moduli space of torsion-free $G_2$ structures.