Recognising the unknot (*Talk will begin at 12:00PM)
Recognising the unknot (*Talk will begin at 12:00PM)

Marc Lackenby, University of Oxford
Online Talk
*Please note the time change to 12:00 PM*
One of the most basic problems in lowdimensional topology is to determine whether a given simple closed curve in 3space is the unknot. This is known as the "unknotting problem". An algorithm to solve it was given by Wolfgang Haken in the 1960s. However, it remains a significant unresolved question whether there is an algorithm that runs in polynomial time (as a function of the number of crossings in a given knot diagram). In my talk, I will discuss what is known about this question. I will explain why the unknotting problem is known to lie in NP and coNP, and I will outline a new unknot recognition algorithm that runs in quasipolynomial time.