(University of California at Davis)
"Recognizing the Unknot"
Abstract:Determining whether a particular curve is knotted is the fundamental problem of knot theory. The search for an algorithm to solve this problem goes back to Max Dehn in 1910, and has historical ties to the development of the theory of algorithms. The first algorithm was found by Haken, fifty years later.
I will discuss some recent advances in determining the complexity, or running times, of algorithms to solve this type of problem. I will also discuss a recent probabilistic approach which gives a "Zero knowledge proof" that certain curves are knotted.