For more information about this meeting, contact Anatole Katok, Aaron Brown, 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
|Date:||11 / 26 / 2012|
|Time:||03:30pm - 05:30pm|