For more information about this meeting, contact Anatole Katok, Stephanie Zerby, Federico Rodriguez Hertz, Boris Kalinin.

Title: | The Statistics of Self-Intersections of Closed Curves on Orientable Surfaces, I. |

Seminar: | Working Seminar: Dynamics and its Working Tools |

Speaker: | Matthew Wroten, Penn State |

Abstract: |

Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case of closed surfaces) as a cyclic word of minimal length in terms of the fundamental group's generators. The self-intersection number of a conjugacy class is the minimal number of transverse self-intersections of representatives of the class. By using Markov chains to encapsulate the exponential mixing of the geodesic flow and achieve sufficient independence, we can use a form of the central limit theorem to describe the statistical nature of the self-intersection number. For a class chosen at random among all classes of length n, the distribution of the self intersection number approaches a Gaussian when n is large. This theorem generalizes the result of Steven Lalley and Moira Chas to include the case of closed surfaces. |

### Room Reservation Information

Room Number: | MB216 |

Date: | 10 / 15 / 2013 |

Time: | 03:30pm - 06:00pm |