# Mathematics Colloquia and Seminars

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### Components of Hurwitz spaces

**Geometry/Topology**

Speaker: | Brian Osserman, UC Davis |

Location: | 1147 MSB |

Start time: | Wed, Feb 6 2008, 4:10PM |

Hurwitz studied branched covers of the Riemann sphere, which can be described equivalently in either geometric or group-theoretic terms. Moduli spaces of such covers are now known as Hurwitz spaces, and a fundamental question has been to understand the connected components of Hurwitz spaces. This question has fundamental applications in algebraic geometry and number theory. I will discuss some recent work on the topic, as well as directions for further research.