The homogeneity conjecture for supergravity backgrounds

Understand

These notes record three lectures given at the workshop "Higher symmetries in Physics", held at the Universidad Complutense de Madrid in November 2008.

• In them we explain how to construct a Lie (super)algebra associated to a spin manifold, perhaps with extra geometric data, and a notion of privileged spinors.
• The typical examples are supersymmetric supergravity backgrounds; although there are more classical instances of this construction.
• We focus on two results: the geometric constructions of compact real forms of the simple Lie algebras of type B_4, F_4 and E_8 from S^7, S^8 and S^15, respectively; and the construction of the Killing superalgebra of eleven-dimensional supergravity backgrounds.