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Catching the Culprit: A Hard Unknot by Darin Li '22, Mathematics Colloquium

Mon, December 6th, 2021
1:00 pm
- 1:45 pm

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Catching the Culprit: A Hard Unknot by Darin Li ’22, Mathematics Colloquium, Monday, December 6, 1 – 1:45 pm, North Science Building 113, Wachenheim

Abstract:  The fundamental question of knot theory is how to tell two knots apart.  We tackle a particular case of this question: how do we tell an unknot apart from a knotted knot?  On first glance, many examples of unknots are easy to solve, but we examine a famous “culprit” that is hard to solve.  Could we know it is the unknot reliably?  First, this talk will lay out a theory by which we can understand knots as continued fractions. Second, it will synthesize several major results from knot theory to develop an unknot test.  Finally, we will use the unknot test to catch the culprit, and a drawn solution of the culprit will be presented.

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