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### On loops intersecting at most once

**Geometry/Topology**

Speaker: | Joshua Greene, Boston College |

Related Webpage: | https://www2.bc.edu/joshua-e-greene/ |

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.