Resonance and Koszul modules in algebraic geometry

Inspired from ideas in topology, Koszul modules and the associated resonance varieties turned out to have important algebro-geometric applications for instance to (i) Green’s Conjecture on syzygies of canonical curves, (ii) stabilization of cohomology of projective varieties in arbitrary characteristics and (iii) Chen invariants of hyperplane arrangements. I will discuss new developments related to this circle of ideas obtained in joint work with Aprodu, Raicu and Suciu.