The Classification of Extended Topological Field Theories -Jacob Lurie 

Physicist: A TQFT is an action form we diffentiate w.r.t. It has to be independent of the metric, hance "topological". Mathematician: A TQFT is a d-functor between the full coobardism d-category into a different d-category who may have C-vector spaces for object. Also sometimes it's a (d,info)-category with graded algebras, and sometimes it's something else.

Absolutely glorious. Everyone needs to hear convos between Lurie, Witten, Maldacena and Moore.

This needs more views 😎💭☘️

He has fields medal level talent. Luck plays an important role in life. He does not think about awards. He likes math.

Thank you

Does anyone once calculate the result of the partition function acts on the torus (based on Atiya's definition)? Don't we need to know more about the structure of the Frobenius algebra？

The goat.

I keep getting 1 for the torus, and 1/tr1 for the next genus up, etc., after picking something reasonable for the map g : A -> A×A (given by pair of pants). I'm not really sure how to "restrict" the mapping enough to unambiguously get these results.

why isnt this trending?

Good

10:24 Are you trying to say the knot itself holds itself together? Is this some sort of mathematical metaphor for crochet? 12:40 I take this to mean you are going with a thread, not a string or a strand; but I suppose all would have an orientation. Tying in a pattern without regard to material. 18:26 Material without regard, except for the thread, string or strand sliding off the knitting needles, which could be many knitting needles, or many types of thread, string or strands. 24:14 No, not many knitting needles. Just passing back that way, connecting, then departing, which would mean one thread, string or strand can hold its own knot. It would just have to reappear at a junction before another departure. 18:22 I can get a loop out of one thread, string or strand. 39:57 The only which way it matters to go is one of two ways as long as those two ways return or wrap and cannot run infinitely parallel. 50:12 I take it you're just jamming them together by force, an infinite amount of force, when the whole of it wants to remain inert or repel. 52:28 Now definable amount of force. 54:42 _No sense in untying a knot._ I thought we were trying to Classify these Fields. 57:52 Now I can see the crystal, how do you say, it? Lattice. Which can extend from a knot in the center. Like snowflakes. But without lines, waves. Snowflakes made of waves. The structure would just be whipping with crossing knots. 1:04:28 It just sort of melted in front of me. 1:05:08 Can we make it solid again? 1:05:54 Knots collapse. 1:09:45 What is done can't be undone, son. Not in any way it wouldn't just be a mess. That's chaos!

Oh my god, how do you differentiate w.r. vector?

Our manifold is almost certainly.... Sin(cos(u/2)cos(v/2),cos(u/2)sin(v/2),sin(u)) 0