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University Park
Altoona

Thursday, December 14, 2006
5:30pm, 260 Hawthorn

Kasra Rafi
University of Connecticut

Divergence rate of geodesics in Teichmüller space and mapping class groups.

Abstract: We say a function f(R) is a divergence function for two geodesic rays in a metric space that share a basepoint if points on these rays that are distance R from the basepoint can be connected along a path that remain distance at least R from the basepoint and has length less than f(R). We show that every two geodesic rays in the Teichmüller space that share a basepoint have a quadratic divergence function. Furthermore, we show that this esmiate is sharp by providing examples where every divergence function is at least quadratic. The same is also true for geodesic rays in the mapping class group. (Joint work with Moon Duchin)..

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We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2006 semester: Aissa Wade and Wojciech Dorabiala.

 

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