Research project: Massey products in toric topology
This work is about understanding properties of Massey products in the cohomology of moment-angle complexes from a combinatorial perspective. Moment-angle complexes, one of the main objects in toric topology, have a natural underlying combinatorial structure that allows us to study these topological spaces by understanding their corresponding simplicial complex. There are many applications of Massey products in topology; they determine differentials in spectral sequences, are obstructions to formality of spaces, etc. As higher cohomology operations, Massey products are extremely difficult to compute. Fortunately, the combinatorial structure of moment-angle complexes (or more generally, polyhedral products) lends nicely to the study of Massey products in the cohomology of such spaces.