Invariants of abelian covers

In this talk I will define several invariants of abelian covers of spaces. I will state (and, hopefully, prove) theorem by Papadima and Suciu relating finiteness of abelian covers to plane sections of resonance varieties, and discuss some ways of computing Bieri-Neumann-Strebel invariants for formal spaces.
Familiarity with basics of rational homotopy theory will be convenient for audience, but not mandatory.