For more information about this meeting, contact Anatole Katok, Dmitri Burago.
| Title: | The Statistics of Self-Intersections of Closed Curves on Orientable Surfaces |
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| Seminar: | Center for Dynamics and Geometry Seminar |
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| Speaker: | Matthew Wroten, SUNY, Stoney Brook |
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| Abstract: |
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| 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 |
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| Date: | 11 / 26 / 2012 |
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| Time: | 03:30pm - 05:30pm |
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