The minimal Hirsch-Brown model for moment-angle complexes

In this talk we will describe certain higher cohomology operations induced by the torus action on a moment-angle complex. Focusing on examples, we explain how these operations assemble into an explicit Hirsch-Brown model of the torus action and can be used to give a combinatorial description of the minimal free resolution of Stanley-Reisner rings. Time permitting, we will indicate the relevance of these operations to cohomological rigidity and outline a proof that B-rigid simple polytopes are closed under products. This talk is based on joint work with Benjamin Briggs.