The Dehn surgery characterisation problem

Short introductory talks.

A slope p/q is characterising for a knot K in the 3-sphere if the oriented homeomorphism type of the 3-manifold obtained by performing Dehn surgery of slope p/q on K uniquely determines the knot K. In this talk, I will outline our current understanding of characterising and non-characterising slopes and discuss some new ideas for distinguishing them.