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TQFTs via Planar Algebras

So today I am giving a talk in the Subfactor seminar here at Berkeley, and I thought it might by nice to write my pre-talk notes here on the blog, rather then on pieces of paper destined for the recycling bin. 1,520 more words


SF&PA: Temperley-Lieb as a planar algebra

Last week I talked about the Temperley-Lieb algebra – the algebra of boxes with n top points connected in a non-crossing way to n bottom points, with multiplication as stacking boxes.   423 more words


SF&PA: One more example

Sorry for the delay, Scott’s been in town and so I’ve been too busy doing actual research to get much blogging done. This post was also a little delayed because I didn’t understand this example as well as I’d hoped. 651 more words

SF&PA - the Temperley-Lieb algebra

Hi all,

First, I’d like to thank the organizers for inviting me to post on their blog, and apologize for the low tech pictures in what follows. 440 more words


SF&PA: An example

Alright, let’s try to build a bi-oidal category with a good theory of duals. The dumbest possible way to do this is to start with a good monoidal category and put in meaningless labels by hand to make it bi-oidal. 222 more words


SF&PA: What is a Subfactor?

By a subfactor I will mean a pair of rings A < B, such that (and I apologize in advance if I mess this up, as I said I don’t know any analysis): 651 more words


SF&PA: How complicated are groups?

One more warmup post before I get to actual Subfactors. If you were asked to rank finite groups in order of how complicated they were, what measurement would you use? 633 more words