Harvard mathematician Barry Mazur has many new things up on his web-site. These include an expository article on motives (this via David Corfield), and a foreword to a forthcoming popular book called Fearless Symmetry : Exposing the Hidden Patterns of Numbers. This book looks to be the first popular book to deal with the modern use of group representations in number theory, explaining what reciprocity laws are and a bit about the Langlands program.
The concept of a motive and that of using representations of Galois groups constructed using things like motives are two of the most important ideas in modern number theory. Some of the latest developments in this field concern extensions of the Langlands program involving p-adic modular forms. Mazur and Buzzard are teaching courses on this topic, and Mazur has put some lecture notes up on his course web-site. These courses are part of a special semester on Eigenvarieties at Harvard.
Nature has a short article entitled Physicists told to confront those big questions about the Foundational Questions Institute call for proposals. There’s a very positive quote about this from Lee Smolin, who is on the advisory board, but also a much more skeptical one from Paul Steinhardt: “Metaphysics is running rampant through string theory and cosmology,” he says. “I would like to see things go a little bit in the other direction.”
Kimball Martin’s web-site of Exceptional MathReviews includes one by Robert Oeckl about a paper of the Bogdanovs. For more about them see here, here, here, and here. Remarkably, they seem to have some support from at least one string theorist.
The High Energy Physics Advisory Panel (HEPAP) is meeting today and tomorrow in Washington. Presentations there will include one from Bush’s science advisor, John Marburger, and should be available on-line soon.
This weekend, the Mathematical Sciences Research Institute (MSRI) will be dedicating its new building, named after Shiing-Shen Chern. As part of the festivities, Roger Penrose will be giving talks, including a public lecture Sunday on Fashion, Faith and Fantasy in modern theoretical physics.
The second LHC Olympics were recently held at CERN and the talks are available on-line. This is a rather unusual exercise designed to get string theorists and other not-so-hardcore phenomenologists involved in analyzing simulated LHC data. There seem to me to be two big problems with this. First of all, there are no backgrounds in this simulated data, and understanding these backgrounds is going to be the main problem with the LHC data for quite a while. It will be the experimenters who will have to do this, and they may need help from theorists, but help of a very different nature than what this exercise is aiming at. Secondly, once backgrounds are understood and potential signals are extracted, I doubt that the LHC experimenters will be releasing the kind of data simulated here for use by theorists. I suspect they’ll be doing the kind of analysis going on at the LHC Olympics themselves and releasing the results as papers under their own names. For more about this, see postings by Lubos here and here. The first of these drew the following comment from a European phenomenologist:
Phenomenology has been always been strong in Europe, hundreds of ppl work in this field since decades, and most consider this contest as child’s play. Guess why no European team took part in this activity, right within a truly European institution which has scores of local phenomenologists? It is a bit like if a few phenomenologists decide to learn string theory and organize a contest in Princeton about who can build the best string model….
While this exercise is unrealistic, it may at least clarify various issues about how testable certain specific scenarios really will be at the LHC.
The latest Seed Magazine has some interesting articles. One about mathematical proof discusses problems with proofs in mathematics that may be too complicated to be properly refereed, especially the recent work by Thomas Hales on the Kepler conjecture. It ends with a depressingly silly comment by Keith Devlin:
I see a parallel between the uncertainty of these proofs and developments in physics like string theory, where we’re developing mathematical theories of matter that may forever remain elusive to experimental verification.
This is the same kind of foolishness as the comment that “physicists may have to rethink what it means for a theory to explain experimental data” because of string theory (see here).
Another Seed article that has gotten a lot of attention because of it’s topic is one called Getting Physical about physicists and sex. See commentary here, here and here. This last link is to Jennifer Ouellette’s new blog Cocktail Party Physics, which is of independent interest.