Mathematics Colloquia and Seminars

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Description

There are 352.2 million prime knots in the 3-sphere with at most 19 crossings.  In joint work with Sherry Gong, I studied which of these knots are slice, in both the smooth and topological categories. While no algorithm is known for deciding whether a given knot is slice in either setting, we were able to determine it smoothly for all but about 11,400 knots (0.003% or 1 in 30,000) and topologically for all but about 1,400 knots (0.0004% or about 1 in 250,000). In particular, we showed that some 1.6 million of these knots (0.46%) are smoothly slice (in fact ribbon) and that 350.5 million are not even topologically slice (99.54%).  I’ll discuss the varied tools and techniques we used for this, and explain how our data is consistent with several important conjectures and suggests new ones.