Either finite-type invariants distinguish oriented knots, or they do not distinguish prime, unoriented knots

This talk will (hopefully) be a gentle introduction to the topic of finite-type invariants of knots and 3-manifolds. In the case of knots, they are also called Vassiliev invariants. It is not known whether
Vassiliev invariants distinguish all knots from each other. Nonetheless, we can conclude from their basic properties that they either distinguish all oriented knots, or they do not distinguish prime, unoriented knots.
I will discuss this issue and other aspects of finite-type invariants and maybe TQFT invariants in 3-dimensional topology.