# 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.