This is the first post in a many part series of posts on Subfactors and Planar Algebras. The study of Subfactors is a topic in the theory of Von Neumann algebras which at first might seem very far from our blog’s usual topics. However, it turns out to be intimately related to quantum algebra and higher category theory. In fact, at Berkeley almost everyone who studies quantum groups or related topics also learns at least the rudiments of Subfactors (due largely to Vaughan Jones’s excellent Subfactor seminar). Since algebraists outside of Berkeley don’t seem to get as much exposure to this beautiful topic, hopefully all you out there in internet land will enjoy learning a little bit about it. I’ll be taking a very indeosyncratic representation theory approach to the topic, and so it should be accessible to people who (like me) know very little analysis.
I’m also very happy to welcome our friend and colleague Emily Peters who will be guest blogging on this topic. She’s a 5th year graduate student at Berkeley working with Vaughan Jones. Emily’s main research is on the Haagerup subfactor, which makes her far more expert on subfactors than I. She’s collaborating with Scott Morrison and me on a knot theory/subfactor topic which we may have more to say about in the future. Perhaps most importantly the back of Emily’s head features prominently on an certain illustrious math blog.
I hope to put up the a few posts with mathematical content on this topic up in the next few days.