Speaker: Elizabeth Denne, Harvard University
Title: Alternating Quadrisecants of Knots

Abstract: It is known that for every knotted curve in space, there is a line intersecting it in four places, a quadrisecant. Comparing the order of the four points along the line and the knot we can distinguish three types of quadrisecants; the alternating ones have the most relevance for the geometry of a knot. I will show that every (nontrivial tame) knot has an alternating quadrisecant. This result has applications to the total curvature, second hull and ropelength of knots.