The Columbia Math department has been doing extremely well in recent years, with some wonderful mathematicians joining the department. A couple items first involving some of them:
- Kevin Hartnett at Quanta Magazine has a great article about developments in the field of technical issues in the foundations of symplectic topology. This explains work by my colleague Dusa McDuff, who together with Katrin Wehrheim has been working on such issues, trying to resolve questions raised by fundamental work of Kenji Fukaya and collaborators. For technical details, two places to start looking are here and here.
The Hartnett story does an excellent job of showing one aspect of how research mathematics is done. Due to the complexity of the arguments needed, it’s not unusual for early papers in a new field to not be completely convincing to everyone, with unresolved questions about whether proofs really are airtight. The way things are supposed to work, and how they worked here, is that as researchers better understand the subject proofs are improved, details better understood and problems fixed. Along the way there may be disagreements about whether the original arguments were incomplete or not, but almost always people end up agreeing on the final result.
Also featured in the article is another of my Columbia colleagues, Mohammed Abouzaid, who provides characteristically wise and well thought out remarks on the story.
- Via Chandan Dalawat, I learned of an interesting CIRM video interview with another colleague, Michael Harris. The same site has this interview with Dusa McDuff, as well as a variety of other interviews in English and French.
For some other non-Columbia related links:
- The 70th birthday of Alain Connes is coming up soon, and will be celebrated with a series of public lectures and conferences on noncommutative geometry in Shanghai.
This year will be the last series of lectures by Connes at the College de France. They’re appearing online here, and I highly recommend them. He’s taking the opportunity to start the series with a general overview of the point of view about the relationship of geometry and quantum theory that he has been developing for many years.
- For employment trends in theoretical particle physics, there are some updated graphs of data gleaned from the particle theory jobs rumor mill created by Erich Poppitz and available here. In terms of total number of jobs, there has been some recovery in the past couple years, with about 15 jobs/year, above the 10 or so common since the 2008 financial crisis (before 2008 numbers were higher, 20-25). As always, an important thing to keep in mind about this field is that this number of permanent jobs/year is a small fraction of the number of Ph.Ds. in the subject being produced each year at US universities.
The numbers for distribution of subfields separate out “string theory” and lattice gauge theory. There have always been few jobs in lattice gauge theory, appear to be no hires in that subject for the past two years. I’m putting “string theory” in quotes, because it’s very hard these days to figure out what counts as “string theory”. With Poppitz’s choice of what to count, hiring in string theory has recovered a bit, now around 25% of the total for the past two years, up from more like 15% typical since 2006 (earlier on the numbers in some years were around 50%).
- As pointed out here by commenter Shantanu, on Wednesday John Ellis gave a talk on Where is particle physics going? at Perimeter. I’d characterize Ellis’s answer to the question as “farther down the blind alley of supersymmetry”. He spins the failure to find SUSY so far at the LHC as some sort of positive argument for SUSY. The question session was dominated by questions about SUSY, with Ellis taking the attitude that there’s no reason to worry about the failure so far of the fine-tuning argument for SUSY, all you need to do is “ratchet up your pain threshold”. I fear that’s some sort of general advice where this line of research is going.
About the failure to find any evidence for SUSY wimps that were supposed to explain dark matter, Ellis explained that he had been working on this idea for 34 years, first writing about it in 1983, so with that much invested in it, he’s not about to give up now.
Update: Davide Castelvecchi points me to another new mathematics story at Nature.
Update: One more. A profile of Roger Penrose by Philip Ball. Penrose explains that his main problems with string theory come from two sources. One is the instability problem of extra dimensions, the other is his aesthetic conviction that sticking to four space-time dimensions is a good idea since it is only in four dimensions that you get the beautiful geometry of twistors. Ball raises the interesting question of whether Penrose could have a successful scientific career if he were starting out today:
Worst of all, the career structures and pressures facing young researchers make it increasingly hard to find the time simply to think. According to several early-career scientists interviewed by Nature, the constant need to bring in grant money, to produce papers and administer groups, leaves little time to do any research, still less indulge anything so abstract and risky as an idea.