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Topology/Geometry Seminar

Statistics for random curves

Tarik Aougab (Haverford College)

Location:  Hill 705
Date & time: Tuesday, 03 March 2020 at 3:50PM - 4:40PM

For S a finite type orientable surface, we study random walks on the Cayley graph of the fundamental group associated to a finite generating set. In particular we show that generically, the self-intersection number of a curve is bounded from above and below by the square of its word length, and we obtain bounds on the lifting degree (the minimum degree cover to which the curve admits a lift with no self-intersection) and the minimum geodesic length of the curve in any complete hyperbolic metric on the surface. We apply this to study bounds due to Dowdall, relating the dilatation of a point-pushing pseudo-Anosov to the self-intersection number of the defining curve, and we prove that generically, these bounds can be dramatically improved. This represents joint work with Jonah Gaster.

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