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On loops intersecting at most once


Speaker: Joshua Greene, Boston College
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Location: 3106 MSB
Start time: Tue, Oct 29 2019, 1:30PM

How many simple closed curves can you draw on the surface of genus g in such a way that no two are isotopic and no two intersect in more than k points? It is known how to draw a collection in which the number of curves grows as a polynomial in g of degree k+1, and conjecturally, this is the best possible. I will describe a proof of an upper bound that matches this function up to a factor of log(g). It is based on an elegant geometric argument due to Przytycki and employs some novel ideas blending covering spaces and probabilistic combinatorics.