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Caltech/USC/UCLA Joint Topology Seminar

Monday, March 9, 2020
5:00pm to 6:00pm
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Linde Hall 310
On loops intersecting at most once
Joshua Greene, Department of Mathematics, Boston College,

How many simple closed curves can you draw on the closed 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 involves hyperbolic geometry, covering spaces, and probabilistic combinatorics.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].