Talk by Dr. Kate Petersen (Dept of Mathematics, Florida State University)

3/14/2019   Wilson Hall 1-123   4:10-5:00pm


The SL(2,C) character variety of a 3-manifold M is an algebraic set that is basically the moduli space of all hyperbolic structures on M.  By Mostow-Prasad rigidity most of these are not complete.  Nonetheless, the character variety encodes a wealth of information about M.  Famously, Culler and Shalen used Bass-Serre theory to show that ideal points of the character variety detect surfaces in the manifold.  More recently, there are several conjectural relationships between the character variety and quantum invariants. I’ll introduce the character variety and highlight the role of symmetries in understanding its structure and many of the properties it encodes.