M2-branes, Einstein manifolds and triple systems

Abstract

This is the written version of a talk given on 1 July 2009 at the XXV Max Born Symposium: the Planck Scale, held in Wroclaw, Poland. I review the possible transverse geometries to supersymmetric M2-brane configurations and discuss the representation-theoretic description of their conjectured dual superconformal Chern-Simons theories.