# Mathematics Colloquia and Seminars

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### Intersections in the character variety

**Geometry/Topology**

Speaker: | David Dumas, University of Illinois at Chicago |

Location: | 1147 MSB |

Start time: | Thu, May 12 2011, 2:10PM |

We will discuss two subvarieties of the SL(2,C) character variety of a compact surface S arising from natural geometric constructions. The first is an algebraic subvariety arising from a 3-manifold with incompressible boundary diffeomorphic to S. The second is an analytic subvariety arising from a Riemann surface diffeomorphic to S and its space of complex projective structures. The main theorem is that these two subvarieties intersect in a discrete set. A corollary is that Thurston's skinning maps are finite-to-one.