Vaughan: Sometimes its really good to make mistakes in mathematics. Ask him.
Abstract. A long time ago I read somewhere that when you write a scientific article you may use the word "very" very freely. Then at proofreading you just have to go over everything a second time and scratch out every, really every, occurrence of that word from your article. Anyway, my talk will be about a class of knotted trivalent graphs which is obviously very 3D and nothing planar, yet it forms a planar algebra. Indeed, a very planar algebra  so planar that unlike, say, tangles, it cannot be generalized to higher genus ambient surfaces. The resulting planar algebra is quite useful  it provides a Reidemeistermove planar context for a universal finite type invariant. I'll mention that and explain a bit, but my main reason for talking about this very nonplanar very planar algebra is simply that it is amusing.
Handout. JavaScript browser, PNG.
Audio. At Fields

