Title: Polynomial time knot theory

Abstract

When are two knots the same and how can you tell quickly?
In joint work in progress with D. Bar-Natan we found a new method to distinguish many knots in polynomial time. As a comparison, most methods take exponential time or worse. The notable exception is the Alexander polynomial and ours is a generalization of that based on solvable approximation of Lie algebras. 

No knowledge of either Lie algebras or topology is assumed. The plan is to first introduce the Lie algebra sl_2 and some of its solvable approximations. Next we show how to place elements of the algebra onto a picture of a knot so their product is independent of the chosen picture of the knot. Actually computing such products efficiently requires a novel calculus of ordered exponentials. Time permitting, we will mention some applications in three and four dimensions.
A handout for this talk will be available at www.rolandvdv.nl/MLA
 

Location: KdVI meeting room, Science Park 107, room R3.20