For more information about this meeting, contact Thomas Barthelme, Anatole Katok, Federico Rodriguez Hertz, Mari Royer, Dmitri Burago.

Title: | Quasigeodesic flows and dynamics at infinity. ATTENTION This meeting is a Dynamical Systems seminar |

Seminar: | Geometry Working Seminar |

Speaker: | Stephen Frankel, Yale University |

Abstract: |

A flow is called quasigeodesic if each flowline is uniformly efficient at measuring distances on the large scale. In a hyperbolic 3-manifold, quasigeodesic flows are exactly the ones that one can study "from infinity." We'll illustrate how the 3-dimensional dynamics of a quasigeodesic flow is reflected in a simpler 1-dimensional discrete dynamical system at infinity: the universal circle. This is a topological circle, equipped with an action of the fundamental group, that lies at the edge of the orbit space of the flow. We will see that one can find closed orbits in a flow by looking at the action on the universal circle. We will also show that the universal circle provides a generalization of the well-known Cannon-Thurston theorem.
The universal circle for a quasigeodesic flow (due to Calegari) has a relative for a pseudo-Anosov flow (Calegari-Dunfield). The content of this talk completes a large part of Calegari's program to show that every quasigeodesic flow on a closed hyperbolic manifold can be deformed, keeping it quasigeodesic, to a pseudo-Anosov flow. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 03 / 19 / 2014 |

Time: | 03:35pm - 04:35pm |