This week in Philadelphia the String-Math 2011 conference is going on, planned as the first of a series, with String-Math 2012 next summer in Bonn. Slides of the talks are appearing here. There’s also supposed to be video, but the saved video seems to require some sort of UPenn login, and I’ve not been able to get the streaming video to work. The public talk by Cumrun Vafa puts out the classic message that strings have come to the rescue of physics, unifying QM and gravity, and that:
Smooth geometry of strings seems to explain all known interactions (at least in principle)
The techinical talks cover a lot of ground, much of it having little to do with string theory. Michael Douglas’s talk surveys problems related to finding non-perturbative formulations of quantum field theory that one might hope to say something precise about, but it contains a lot more questions than answers. I’m most curious about David Ben-Zvi’s talk tomorrow, so hope that slides or video of that will be available.
The circle of ideas relating gauge theories, geometric Langlands, TQFTs and representation theory will be getting even more attention than the mathematics of string theory this summer. In a couple weeks will begin a two-part program at Luminy and then Cargese on Double Affine Hecke Algebras, the Langlands Program, Affine Flag Varieties, Conformal Field Theory, Super Yang-Mills Theory. I don’t know who the author is, but some person or group has written up for the occasion a wonderful summary of the current activity in these and related fields of mathematics, see here. Next month, the KITP will be hosting a program on Nonperturbative Effects and Dualities in QFT and Integrable Systems that will cover some of the same topics.
In some other unrelated news, if you understand French, you can listen to an interesting set of interviews with Pierre Cartier here. Finally, it was announced recently that my colleague Richard Hamilton is sharing this years $1 million Shaw Prize for Mathematics with Demetrios Christodoulou. Congratulations Richard!