PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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

Title:The Statistics of Self-Intersections of Closed Curves on Orientable Surfaces
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Matthew Wroten, SUNY, Stoney Brook
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:MB106
Date:11 / 26 / 2012
Time:03:30pm - 05:30pm