Just time at the moment for some quick links. I’ll start with some math news, since there hasn’t been much of that here recently:
- Matt Baker has the sad news here of the death of Berkeley mathematician Robert Coleman recently, at the age of 59. Coleman was a leader in the field of p-adic geometry, and managed to continuously do important research work despite a long struggle with MS. He was both highly influential and well-loved, be sure to read the comments which contain appreciations from many different mathematicians.
- Also at Matt Baker’s blog is a summary of recent work by Manjul Bhargava and collaborators on the average ranks of elliptic curves. This work shows
at least 20.6% of elliptic curves over Q have rank 0, at least 83.75% have rank at most 1, and the average rank is at most 0.885…
at least 66.48% of elliptic curves overQ satisfy the (rank part of the) Birch and Swinnerton-Dyer (BSD) Conjecture (and have finite Shafarevich-Tate group)
50% of elliptic curves have rank 0, 50% have rank 1, and 0% have rank bigger than 1, and thus the average rank should be 0.5. (And conjecturally, 100% of elliptic curves satisfy the BSD conjecture. :))
the best known unconditional results in this direction were that at least 0% of elliptic curves have rank 0, at least 0% have rank 1, the average rank is at most infinity, and at least 0% of curves satisfy the BSD conjecture.
so this is dramatic progress.
- I’ve yet to hear any solid rumors about who will win the 2014 Fields Medals, to be announced at the ICM in August. To my mind, Bhargava is a leading candidate. Others one hears discussed are Jacob Lurie (a question is whether he has a big enough theorem, the one he’s talking about here may not be finished). Often mentioned names whose work I know nothing about are Artur Avila and Maryam Mirzakhani.
- Another area of huge progress in mathematics over the past year or so has been work of Peter Scholze, who is another excellent Fields Medal candidate, but one young enough that this might get put off until 2018. I’ve been hoping to understand his results on torsion classes in Langlands theory well enough to say something sensible here, but I’m definitely not there yet, maybe some day in the future. In the meantime, watch his extremely clear lectures at the IAS (here, here and here) as well as the talks at this recent MSRI workshop.
- The math community award structure is for some reason prejudiced against the middle-aged, with the high-profile prizes going to the young (Fields Medals) and the old (Abel Prize). This year’s Abel Prize went to Yakov Sinai, and again, I’m in no position to explain his work. However Jordan Ellenberg was, and there’s video here of the prize announcement, including Ellenberg’s talk about Sinai’s work. In the past Timothy Gowers gave such talks, with not everyone happy about this. No news yet on whether Sowa will change his blog name to Stop Jordan Ellenberg! !!!.
- Leila Schneps is trying to raise funds for an English translation of the 3rd volume of Winfried Scharlau’s German language biography of Grothendieck. Go here to contribute, I just did.
Turning to physics news:
- the recent BICEP2 data is still attracting a lot of attention. Initial news stories were often dominated by nonsense about the multiverse, more recent ones are more sensible, including Adrian Cho at Science Magazine, Clara Moskowitz at Scientific American, and a George Musser interview with Gabriele Veneziano.Yesterday Perimeter hosted a workshop on implications of BICEP2. The theory talks I looked at didn’t seem to me to have much convincing in them, except that Neil Turok acknowledges that this kills off the Ekpyrotic (bouncing brane) Universe and he’s paying off a $200 bet. For some reason, Nima Arkani-Hamed now seems to speak at every single fundamental physics meeting, so was also at this one. More interesting were the experimental talks, with new data soon on its way, including Planck results planned for October, possibly measuring r to +/-.01 (BICEP2 says r=.20).
- For some perspective on inflationary theory, CU Phil in recent comment section points to a new volume on the Philosophy of Cosmology. It includes some great articles putting multiverse mania in context by George Ellis and Helge Kragh, as well as an enlightening discussion of the issues surrounding inflationary theory, especially “Eternal Inflation”, from Chris Smeenk.
- For the latest news about LHC results coming in from the Run 1 dataset, see this report from the Moriond conference.
- Finally, physics continues to inspire frightening movie projects, see here.