The cohomology jump loci of a space are of several types: the characteristic varieties, defined in terms of homology with coefficients in rank one local systems; the resonance varieties, constructed from information encoded in the cohomology ring; and the complements to the Bieri-Neumann-Strebel-Renz invariants, which are defined in terms of Novikov-Sikorav homology. In this talk, I will explore the geometry of these sets and the delicate interplay among them, especially in the context of compact, orientable 3-manifolds.

Notes attached. Speaker(s): Alex Suciu (Northeastern University)