Musing over algebraic models for the cohomology of moment-angle complexes

Reporting on an ongoing joint work with Martin Bendersky.
Describing the cohomology of (real and complex) moment-angle complexes (in their many guises) has been a motivating problem that has driven research developments in a host of mathematical areas; commutative algebra, combinatorics, configuration spaces, algebraic geometry, toric topology, just to name a few.
In the talk I shall recall some of algebraic models and illustrate that, although seemingly different, they have the same direct interpretation in geometry of constitutional topological spaces and combinatorics of simplicial complexes.