## University of Sydney Algebra Seminar

# Alex Dimca (Université de Nice - Sophia Antipolis)

## Friday 22nd March, 2:30-3:20pm, Carslaw 273

### Characteristic varieties and resonance varieties

The characteristic varieties encode the dimensions of the twisted cohomology groups of a space \( X\). The resonance varieties encode the dimensions of the cohomology groups of Aomoto complexes \(A^*_a=(H^*(X), a \cup)\) built with the cohomology algebra \(H^*(X)\). In many cases (e.g. \(X\) is a projective complex manifold or \(X\) a hyperplane arrangement complement), the relation between the two types of varieties is rather simple. In this talk I discuss the general case when \(X\) is a smooth quasi-projective manifold.