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### Picard groups of moduli spaces of curves with symmetry

**Geometry/Topology**

Speaker: | Kevin Kordek, Texas A&M |

Location: | 2112 MSB |

Start time: | Mon, Apr 17 2017, 1:10PM |

In 1966, Mumford showed that the (orbifold) Picard group of the moduli space of genus g Riemann surfaces is isomorphic to the second integral cohomology of the genus g mapping class group. Technology developed since that time now allows one to productively study various generalizations of Mumford's original calculation. In this talk, I will explain how the theory of symmetric mapping class groups, developed by Birman-Hilden, Harvey, and others, can be used to understand - and sometimes exactly compute - the Picard groups of various moduli spaces of curves with symmetry, for example the moduli spaces of hyperelliptic curves.