Knot Theory


This research presents the experience of standing inside of a knot, from the simplest trefoil knot (the kind of knot you tie your shoes with) to arbitrary numbers of windings (even fractional) in multiple dimensions. As the knot winds around us, we can also adjust the writhe, or cabling, around the knot itself. We visualize and sonify the knot’s “intrinsic energy” and can watch as it gradually relaxes into its lowest energy configuration for optimal embedding in space. We can also see and adjust the Hopf fibers around which the knot winds. We are just beginning to investigate some of the more complicated aspects of even the simplest knots.

Key faculty, postdoctoral, and graduate student researchers associated with the project: Dr. Pablo Colapinto, Professor JoAnn Kuchera-Morin.