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Joshua Greene, RLM 12.166: On loops intersecting at most once
Monday, November 11, 2019, 02:00pm - 03:00pm
How many simple closed curves can you draw on the surface ofgenus g in such a way that no two are isotopic and no two intersectin more than k points? It is known how to draw a collectionin which the number of curves grows as a polynomial in g of degreek+1, and conjecturally, this is the best possible. I will describea proof of an upper bound that matches this function up to afactor of log(g). It is based on an elegant geometric argumentdue to Przytycki and employs some novel ideas blending coveringspaces and probabilistic combinatorics.
Location: RLM 12.166

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