USA Topology Seminar
Permanents and the Jones polynomial
Iain Moffatt, University of South Alabama
Details
Friday, September 18, 2009
ILB 370
1:00-2:00 pm
Abstract
The permanent of a square matrix is defined in a way similar to the determinant, but without using signs. The exact computation of the permanent is hard, but there are Monte-Carlo algorithms that can estimate general permanents. Given a planar diagram of a link L with n crossings, we define a 7n-by-7n matrix whose permanent is equal to the Jones polynomial of L. This result accompanied with recent work of Freedman, Kitaev, Larson and Wang provides a Monte-Carlo algorithm to any decision problem belonging to the class BQP, i.e. such that it can be computed with bounded error in polynomial time using quantum resources.