Moore's Conjecture for polyhedral products

In the early 1980's John Moore posed a conjecture which, if true, would establish a deep connection between the rational and torsion homotopy groups of simply-connected finite dimensional spaces. In this talk we show that Moore's Conjecture holds for generalised moment-angle complexes, and go on to characterise those polyhedral products which have finitely many rational homotopy groups. This is joint work with Y. Hao and Q. Sun.