Title: Resonance schemes, Koszul modules, and Hilbert series
Speaker: Alex Suciu
Location: Sala 306–307 “Constantin Bănica”, Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Abstract: 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.