For more information about this meeting, contact Anatole Katok, Dmitri Burago.

Title: | Gap Distributions and Homogeneous Dynamics |

Seminar: | Center for Dynamics and Geometry Seminars |

Speaker: | Jayadev Athreya, University of Illinois at Urbana-Champaign |

Abstract: |

The Farey sequence F(Q) is the collection of fractions
between [0,1] whose denominator (when written in lowest terms) is at
most Q. As Q grows, these points become uniformly distributed in the
interval, so in some sense, look `random'. However, when you look at
the gaps between them, they do not behave like those for uniformly
distributed random variables, but instead follow an unusual law known
as Hall's Distribution. We will explain a proof of this result that
uses horocycle flow on the space of lattices SL(2,R)/SL(2, Z), and,
time permitting discuss how this picture can be generalized to
understanding gaps between directions of saddle connections on Veech
surfaces. This talk will include elements from joint work with Y.
Cheung, joint work with J. Chaika, and joint work with J. Chaika and
S. Lelievre. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 11 / 05 / 2012 |

Time: | 03:30pm - 05:30pm |