**Kathleen Petersen**

Florida State University, USA

March 2, 2017

**Character varieties of 3-manifolds**:
The (P)SL(2,C) character variety of a 3-manifold M is essentially the set
of representations of the fundamental group of M into (P)SL(2,C) up to
conjugation. This algebraic set encodes a lot of data about M. For
example, Culler and Shalen showed that using Bass-Serre theory, surfaces in M can be `detected' by points on the character variety. It is also conjecturally related to the colored Jones polynomial via the AJ conjecture. I'll introduce this set and talk about some results about the structure of this set, like how many irreducible components does it have, and how is the geometry of the character variety related to the topology of the M.