Thursday, May 21, 2026 - 16:00 in V2-210/216
A tale of three unknotting conjectures
A talk in the Mathematisches Kolloquium series by
Susan Hermiller from University of Nebraska
| Abstract: |
A knot is a circle embedded in 3-space; two knots are considered to be the same if we can deform one to the other, without breaking the circle or letting it pass through itself. Unknotting number is a fundamental measure of how complicated a knot is, measuring how far it is from the unknot via crossing changes. Unknotting number is a challenging invariant to compute; a vast array of tools have been applied to its calculation, and many conjectures have grown up around it. In this talk I will discuss three conjectures, each aimed at simplifying the task of computing unknotting numbers. I will describe how our resolution of one of these conjectures several years ago led us recently to resolve another - the (non)additivity of unknotting number under connected sum. This is joint work with Mark Brittenham.
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