Hopf algebra gauge theory and Kitaev models at Perimeter Institute

I just got back from a trip to the Perimeter Institute, where I spoke at a conference on Hopf Algebras in Kitaev’s Quantum Double Models.

This workshop was a lot of fun!  I learned a lot, had the chance to talk to people I’ve known for a long time, and meet others I hadn’t managed to connect with before. I was especially excited to find out about some lines of work in progress that build on my work with Catherine Meusburger on Hopf algebra gauge theory.

In fact, our work on this seems to have been an impetus for the workshop, and it was really gratifying to see how other people are beginning to apply our theory, and also work out some interesting examples of it for particular Hopf algebras!  I’m anticipating some interesting work coming out in the near future.

Here’s the conference photo; I’m farthest right, and my coauthor, Catherine, is the 11th head from the left, peeking out from the second row:

Hopf-algebras-in-Kitaev-Models-conference-photo

I gave an introductory talk on the subject of Hopf algebra gauge theory, and you can download the slides from my talk, or even watch the video.  Catherine’s talk followed mine, and she showed how Kitaev models are related to Hopf algebra gauge theory in the same way that Turaev-Viro TQFTs are related to Reshetikhin-Turaev TQFTs.  Video of her talk is also available.  Of course, for more detail on Hopf algebra gauge theory, you can also check out our paper: Hopf algebra gauge theory on a ribbon graph.

I can also recommend watching other talks from the conference, available from the webpage linked to above.  This was just the kind of conference I like best, since it brought people from multiple research communities together, in this case including mathematicians and physicists of various sorts as well as mathematical computer scientists. Kitaev models have been a hot topic the past few years, and one reason I think they’re fun is precisely that people from several areas—quantum computation, Hopf algebras, category theory, quantum gravity, quantum foundations, topological quantum field theory, condensed matter physics, and more—are working together.  Of course, this probably also helps explain the rather long conference title.

 

 

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