Not Even Wrong

Update: The America COMPETES Reauthorization has just passed the House and will go to the president to be signed, something no one expected to happen a week or so ago, more details about the legislation here. I gather that it authorizes 5 to 7% increases for science agencies. Problem is that these are not the actual appropriations, which are still up in the air, awaiting action next year by the next Congress. But this does indicate that there is bipartisan willingness to at least pay lip service to protecting the research and development part of the budget.

I learned from a colleague last night about recent events bringing together the topics of the title of this posting, something that one wouldn’t have thought was possible. Last Wednesday there was a showing in Berkeley of Edward Frenkel’s short film Rites of Love and Math, together with the Yukio Mishima film Rites of Love and Death that inspired it. Frenkel is a math professor at Berkeley, and one of the leading figures in geometric Langlands research (which he describes as a “grand unified theory of mathematics”). He’s also a wonderful expositor, almost single-handedly making the beauty of a subject initially renowned for its obscurity accessible to a much wider audience. Recently he has worked with Witten on relations of geometric Langlands to quantum field theory, and with Langlands and Ngo on relations to number theory. At the same time, while a visiting professor in Paris, he co-directed (with Reine Graves) and acted in this new film.

MSRI was one of the two sponsors of the showing of the film, but pulled out of this role recently, for reasons explained here by MSRI director Robert Bryant. He had found that some people in the math community were upset by the film and MSRI’s involvement with it, feeling that it glamorized an objectionable view of the relationship of women to mathematics. There’s a plan to organize some sort of event at MSRI to discuss the issues brought up by the film and the decision to withdraw sponsorship.

I still haven’t seen the film, although I gather that a DVD will soon be available. Congratulations to all involved in this for finding a unique way to make mathematics and mathematicians look interesting and worthy of media coverage. I had no idea it was still possible to stir up controversy in the Bay area with art involving transgressive sex, and would never have thought that using research mathematics was the way to do it.

Update: Andrew Ranicki has written a review of the film for the London Math Society newsletter, available here. He identifies the notorious equation in question (5.7 of http://arxiv.org/abs/hep-th/0610149), and makes the comment that, sartorially, this film is a breakthrough, since, in other films:

By and large, male mathematicians are portrayed as crazies who are smart and lovable, but badly dressed. Likewise for female mathematicians, although they tend to be better dressed. This said, in the film under review, the actors are either very well dressed, or not dressed at all.

I learned this morning from Matin Durrani’s blog that the Perimeter Institute has announced today the first of what they expect to be five very well-funded Perimeter Research Chairs in theoretical physics. The next four will be named after Maxwell, Bohr, Einstein and Dirac (as well as whatever other wealthy individual or organization comes up with funding).

The BMO Financial Group is putting up $4 million and $4 million is coming out of the Perimeter endowment (which is mostly from Blackberry’s Mike Lazaridis). An endowment of $8 million for a chair is quite high. It seems that typical numbers for endowment payouts these days are around 5%, so this would make available $400,000 or so a year to pay some prominent theorist. For comparison, the Simons Foundation has recently announced that it will fund endowed Math+X chairs aimed at mathematicians working at the interface with some other subject. Simons may be the wealthiest hedge-fund manager in the world, but he’s a piker compared to the Canadian financiers, with only $1.5 million going to each chair (to be matched by $1.5 million from the institution that gets the chair, for a total of $3 million). Then again, it just may be that prominent mathematicians are dirt-cheap compared to prominent theoretical physicists.

The Perimeter Institute in recent years has moved away from supporting non-mainstream topics in theoretical physics, while expanding dramatically. The only two conferences announced there for the next year or so are on the topics of LHC physics and AdS/CFT, about as mainstream as one can possibly imagine. If they manage to fund what might be the five highest-paid theoretical physics positions in the world and hire the people they want into them, they will be well on their way to a dominant position in the subject. While, like most industries these days, the tactic here is to shower the top few people in the field with cash, they are also expanding their hiring at more junior levels. According to the rumor mill, last year out of a total of fourteen people hired to tenure-track positions in theoretical particle physics in North America, three of the fourteen went to Perimeter.

For more on this, see here, and an interview with Lazarides and the BMO CEO here.

The December issue of Scientific American is out, and it has an article by Garrett Lisi and Jim Weatherall about geometry and unification entitled A Geometric Theory of Everything. Much of the article is about the geometry of Lie groups, fiber-bundles and connections that underpins the Standard Model as well as general relativity, and it promotes the idea of searching for a unified theory that would involve embedding the SU(3)xSU(2)xU(1) of the Standard Model and the Spin(3,1) Lorentz group in a larger Lie group.

The similarities between (pseudo)-Riemannian geometry in the “vierbein” formalism where there is a local Spin(3,1) symmetry, and the Standard Model with its local symmetries makes the idea of trying to somehow unify these into a single mathematical structure quite appealing. There’s a long history of such attempts and an extensive literature, sometimes under the name of “graviGUT”s. For a recent example, see here for some recent lectures by Roberto Percacci. The Scientific American article discusses two related unification schemes of this sort, one by Nesti and Percacci that uses SO(3,11), another by Garrett that uses E₈. Garrett’s first article about this is here, the latest version here.

While I’m very sympathetic to the idea of trying to put these known local symmetry groups together, in a set-up close to our known formalism for quantizing theories with gauge symmetry, it still seems to me that major obstructions to this have always been and are still there, and I’m skeptical that the ideas about unification mentioned in the Scientific American article are close to success. I find it more likely that some major new ideas about the relationship between internal and space-time symmetry are still needed. But we’ll see, maybe the LHC will find new particles, new dimensions, or explain electroweak symmetry breaking, leading to a clear path forward.

For a really skeptical and hostile take on why these “graviGUT” ideas can’t work, see blog postings here and here by Jacques Distler, and an article here he wrote with Skip Garibaldi. For a recent workshop featuring Lisi, as well as many of the most active mathematicians working on representations of exceptional groups, see here. Some of the talks feature my favorite new mathematical construction, Dirac Cohomology.

One somewhat unusual aspect of Garrett’s work on all this, and of the Scientific American article, is that his discussion of Lie groups puts their maximal torus front and center, as well as the fascinating diagrams you get labeling the weights of various representations under the action of these maximal tori. He has a wonderful fun toy to play with that displays these things, which he calls the Elementary Particle Explorer. I hear that t-shirts will soon be available…

Update: T-shirts are available here.