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Geometry-Topology Seminar

Thursday, September 12, 2019 - 4:30pm

Tarik Aougab

Haverford College


University of Pennsylvania


Given two finite degree regular covers Y, Z of an orientable surface S (not necessarily of the same degree), suppose that for any closed curve gamma on S, some iterate of gamma lifts to a simple closed curve on Y if and only if some (perhaps distinct) iterate of gamma lifts to a simple closed curve on Z. Then we prove that Y and Z are equivalent covers. We’ll discuss connections to Sunada’s construction of isospectral hyperbolic surfaces. This represents joint work with Max Lahn, Marissa Loving, and Sunny Yang Xiao.