Resonance schemes and Hilbert series for Koszul modules

The resonance varieties are cohomological invariants that are studied  in a variety of topological, combinatorial, and geometric settings. I will describe  several conditions that ensure the reducedness of the associated projective resonance schemes and yield asymptotic formulas for the Hilbert series of the corresponding  Koszul modules. For the exterior Stanley–Reisner rings of simplicial complexes,  this approach leads to a relationship between resonance and Hilbert series that  generalizes a known formula for the Chen ranks of a right-angled Artin groups.  Based on joint work with Marian Aprodu, Gavril Farkas, Claudiu Raicu, and  Alessio Sammartano.

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