Despite what one might think at first sight, these three topicshave much in common. Both the first and last were first seriously studiedin the last century in the context of applications to physics, whileFeynman integrals are at once an important tool arising in physics and havebeen used to `prove' many deep results in mathematics while not currentlypossessing a rigorous definition.
In this talk we will demonstrate some of the connections which canbe seen between the three topics by investigating theWitten-Reshetikhin-Turaev invariants of knots and 3-manifolds, and willtouch on some exciting work of the last year which demonstrates that thereis still much structure in this field yet to be uncovered.