Tomorrow morning I’ll head down to Princeton to attend the conference on Gauge Theory and Representation Theory at the IAS. Unfortunately I had to miss the first day of the conference (today), since I would have liked to have heard all the talks, most especially that of Dennis Gaitsgory on local geometric Langlands. Maybe someone who was there will explain to me what he talked about.
That might be even better than attending the lecture, since Gaitsgory’s pedagogical style seems to be rather daunting. Here is an article about his experience teaching linear algebra, and the Harvard Crimson last year ran this frightening account of what it was like to take Math 55 from him. Math 55 is a legendary honors math class for the most fanatical first-year students, and I have fairly vivid memories of my own experience with it (that year it was taught by Konrad Osterwalder and John Hubbard). From what I remember, the first row of the class was occupied by a sizable proportion of the winners of the previous year’s Math Olympiad, and being a rather average student in a math class was a new experience for me. The textbook for the course was a remarkable book by Loomis and Sternberg with the somewhat misleading title Advanced Calculus. It’s now available on-line. Osterwalder made a valiant effort to follow the text during the first semester, while Hubbard more-or-less winged it the second semester, entertaining us by going over in class research papers on dynamical systems and assigning us Spivak’s Calculus on Manifolds as something to work through during the reading period (about a week long) before final exams. Both Osterwalder and Hubbard seem to have been much mellower sorts than Gaitsgory though, since I remember working fairly hard on puzzling out problem sets, but also having a life with quite a lot of other things going on, nothing at all like the experience described in the Crimson article. Kids these days.
The first talk tomorrow morning is supposed to be Maldacena on integrability in N=4 SSYM. He really should be celebrating the day as the 10th anniversary of his amazing paper The Large N Limit of Superconformal Field Theories and Supergravity, which announced the AdS/CFT conjecture and was submitted to the arXiv on November 27, 1997. Work on this conjecture has dominated particle theory in a remarkable way over the last ten years. According to SPIRES, the paper has amassed 4897 citations, at a rate which has only accelerated in recent years, with 551 citations in 2006. It is now the third most heavily cited paper in particle physics, behind only those of Kobayashi-Maskawa and Weinberg. A simple extrapolation suggests that in another four years or so it should become the most heavily cited particle physics paper in the history of the multiverse. Several conferences are celebrating the anniversary, including one next month in Buenos Aires, and another in Fort Lauderdale. Davide Castelvecchi has a quite good popular article on the subject in Science News.
After it’s over, I’ll try and write something about the main topic of the conference, geometric Langlands. In the meantime, my ability to keep the comment section under control may be impaired. Behave.
Update: David Ben-Zvi is putting up his notes from the talks here.