Caltech/USC/UCLA Joint Topology Seminar
Monday, March 9, 2020
5:00pm to 6:00pmAdd to Cal
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].
Event SeriesCaltech/USC/UCLA Joint Topology Seminar Series