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### The space of metric structures on hyperbolic groups

**Geometry/Topology**

Speaker: | Eduardo Oregon Reyes, UC Berkeley |

Location: | 2112 MSB |

Start time: | Thu, Nov 17 2022, 2:10PM |

Hyperbolic groups are generalizations of finitely generated free groups and surface groups, and they act properly and cocompactly by isometries on Gromov hyperbolic spaces. For a fixed hyperbolic group, we can pack all of its actions of this type into a single space, which extends the classically studied Teichmüller and Outer spaces, but contains many more interesting actions. I will talk about this space and some of its properties when it is equipped with a natural metric that resembles Thurston's Lipschitz distance on Teichmüller space. In particular, I will explain how to find many bi-infinite geodesics in this space, which I showed in joint work with Stephen Cantrell.