Exceptional holonomy and related geometric structures: Examples and moduli theory.

We will discuss the constructions of compact manifolds with exceptional holonomy (in fact, holonomy $G_{2}$), due to Joyce and Kovalev. These both use “gluing constructions”. The first involves de-singularising quotient spaces and the second constructs a 7-manifold from “building blocks” derived from Fano threefolds. We will explain how the local moduli theory is determined by a period map and discuss connections between the global moduli problem and Riemannian convergence theory (for manifolds with bounded Ricci curvature).