On the Knotting Probability of Random Equilateral Polygons
Wednesday, June 26, 2019 - 1:30pm - 2:30pm
A n-sided polygon in 3-space can be described as a point in 3n-space by listing in order the coordinates of it vertices. In this way, the space of embedded n-sided polygons is a manifold in which points correspond to piecewise linear knots and paths correspond to isotopies which preserve the geometric structure of these knots. In this talk, we will consider the submanifold of equilateral knots, consisting of embedded n-sided polygons with unit length edges. Using techniques from symplectic geometry, we can parametrize the space of equilateral polygons up to translations and rotations with a set of measure preserving action-angle coordinates. With this coordinate system, we provide new bounds on the knotting probability of equilateral hexagons.