Undergraduate Math Club

Shruthi SridharCornell University
How can we tell if two knots are not the same?

Monday, April 24, 2017 - 4:45pm
Malott 532

Take a piece of untied rope, wrap it around any way you like and stick the open ends together. This is a knot for all purposes of this talk. Except of course, the rope is massless, has zero thickness, and everything else in a physicist’s dream. But all mathematicians care is if 2 knots are the same knot, so we want nice properties for knots that don’t change if we move the knot around in space, and we’d like differentiate knots with these. These properties are called knot invariants, and we’ll explore some important ones: tricolorability, famous knot polynomials like the Jones polynomial and other invariants from geometry and topology.