Poincaré duality and resonance

Thursday, 23 February 2023

Abstract

Every graded, graded-commutative algebra (such as the cohomology ring of a space) determines a family of cochain complexes, parametrized by the elements in degree one of the algebra. The resonance varieties are the loci where the cohomology of these cochain complexes jumps. In this talk, I will discuss some of the constraints imposed by Poincaré duality on the geometry of these resonance varieties.