Knots in the Coxeter Complex $\tilde{B}_3$
Organizers
Speaker
Malors Espinosa
Time
Thursday, May 21, 2026 3:00 PM - 4:00 PM
Venue
A3-4-312
Online
Zoom 518 868 7656
(BIMSA)
Abstract
In this talk we will discuss knots created by galleries in the affine Coxeter complex of type $\tilde{B}_3$. This is a tesselation of Euclidean space with certain pyramids. We bound the stick number by $40$, bu providing an example found by an exhaustive search. We also prove that the smallest length of threefold rotationally symmetric trefoils is $42$. We construct explicit galleries that knot as $9_{35}$, $9_{40}$, $9_{41}$ and $9_{47}$ in a way that has threefold rotational symmetry. Equivalently, we construct words of order three that knot in the desired way. We conclude with three questions inspired by this work. This is joint work with Dylan Burke, Geoffrey Cuff-Chartrand, Mateusz Kazimierczak, and Amin Mobedi.