Not Even Wrong

• For representation theory aficionados, George Lusztig has put on the arXiv a long document with comments on his papers (for a bit more about him, see this).
• For a new idea exemplifying the potential grand unification of mathematics and physics, Minhyong Kim and others have been developing arithmetic Chern-Simons theory (see here and here). There was a recent workshop on the topic, videos of talks available here.
• The editors of the Journal of Algebraic Combinatorics are leaving the Springer journal, setting up a new journal, Algebraic Combinatorics. For more about this, there’s a press release, a story at Inside Higher Education, and a blog entry by Timothy Gowers.
• Landon Clay, founder of the Clay Mathematics Insitute, passed away last week, more about him available here.
• There’s a profile and interview with Carlo Rovelli here.
• While Google continues to develop our new machine overlords, Google money will fund a new IAS program to address their theoretical underpinnings.

I’ve looked at the talks from a few of the HEP experiment and phenomenology summer conferences. If anyone can point me to anything interesting that I’ve missed, please do so. The lack of new physics beyond the Higgs at the LHC has left the field in a difficult state.

One conference going on this past week and next is the IAS PiTP summer program aimed at advanced grad students and postdocs. This year the topic is HEP phenomenology, and talks are available here. If you want to understand the conventional wisdom on the state of the subject, you can watch Nima Arkani-Hamed’s three and a half hour lecture (here and here) which he starts off by describing as on the topic “What the Hell is Going On?”.

A lot of the first part is historical, starting off with the Georgi-Glashow GUT and the arguments for SU(5) or SO(10) GUT unification first put forward 43 years ago. He then walks the audience through the sequence of steps theorists have taken to solve the problems of such models, after an hour ending up at the landscape, spending a half an hour promoting the anthropic solution to the CC and other problems. The second part of the talk is largely devoted to making the case for his favored split SUSY models, with anthropics and the landscape taking care of their naturalness problems. By the end of the three and a half hours, Arkani-Hamed admits that this scenario is not that convincing, while arguing that it’s the only thing he can see left that is consistent with the idea that theorists have been following a correct path since 1974:

It’s the only picture of the world that I know where everything that we learned experimentally and theoretically for the last 30 years has some role to play in it. But my confidence in it is not so super high, and I definitely think its worth thinking about completely radically different things.

The disadvantage to the trajectory of going with what works and then changing a little and changing a little is that you might just be in the basin of attraction of the wrong idea from the start and then you’ll just stay there for ever.

To me by now the evidence is overwhelming that HEP theory has been in the wrong basin of attraction for quite a while, and the overriding question is what can be done to get out of it. If you’re in the wrong basin of attraction, you need to get out of it by going back to the point where you entered it and looking for another direction. I think Arkani-Hamed is right to identify the 1974 GUT hypothesis as the starting point that led the field into this wrong basin. HEP theory has progressed historically by identifying new more powerful symmetry principles. The move in 1974 was to go beyond the SM symmetries by picking a larger gauge group, then breaking it at a very high energy scale with new scalar fields. The history of the last 43 years is that this idea isn’t a successful one: as this talk shows, it leads to an empty theory that explains nothing. Can one find different new ideas about symmetry that are more promising?

I’ve finally found some time to look around the web to see what has been happening at conferences this summer. In this blog post I’ll point to a few on the math/physics interface featuring interesting talks. This area now (I think it may be Greg Moore’s fault) has started to acquire the name of “Physical Mathematics”, to distinguish itself from old-school “Mathematical Physics”. At this point though I’d be hard-pressed to provide a useful definition of either term.

• Talks from last month’s 2017 Bonn Arbeitstagung are available here. This conference was in honor of Yuri Manin and supposedly devoted to Physical Mathematics (although I suspect some of the speakers might not realize that they are doing Physical Mathematics). Dan Freed and Jacob Lurie gave two characteristically lucid series of talks, well worth watching.

  A very active area of physics these days with significant overlap with mathematics (of the sort discussed by Freed) is the study of topological superconductors and other materials in which topology plays a large role. For an introduction to this topic, Davide Castelvecchi at Nature has a new article The strange topology that is reshaping physics.

• CERN has just finished running an institute on the topic of the Geometry of String and Gauge Theories. It included a colloquium talk by Greg Moore on d=4 N=2 Field Theory and Physical Mathematics. I’ve always been fascinated by the d=4 N=2 super Yang-Mills theory in its “twisted” topological version. The mathematics involved is deep and amazing, and it is frustratingly close to the Standard Model…
• Pre-string math 2017 was this past week, and String Math 2017 will be next week. All sorts of interesting talks at both of these, relatively few of which have much to do with string theory. That’s of course also true of Strings 2017, but I’ll write about that elsewhere.

Other suggestions of interesting mathematically related summer schools with talks available are welcome. On the physics side, please wait for a succeeding blog entry on that topic.

Some links to things that may be of interest:

• There’s an excellent article at FiveThirtyEight about the issue of publicizing math research, taking as example the Atlas of Lie Groups and Representations project (which will soon be having a workshop). This kind of thing generally gets no public attention, while at the same time, one of the results of this research arguably got too much public attention (see here).
• There’s a new \$1 million mathematics prize that will be awarded for the first time this fall, together with a $1 million physics prize that was awarded for the first time last year. This is called the Future Science Prize, and to get it you need to be working in China. Used to be a \$1 million prize was a big deal, now with the \$3 million Breakthrough Prizes, a mere million looks like small potatoes.
• Another way you could get a measly \$1 million would be to prove (or disprove) the Hodge conjecture. For some inspiration, see Burt Totaro’s new survey of progress on the Tate conjecture (blog entry here).
• 4 gravitons has a nice posting about work by Turok and others about complexified path integrals and cosmology. The issue of the relation between Euclidean and Minkowski signature QFT is one that I think has gotten far too little attention over the years. Now that I’ve finished writing a book with a QFT discussion that sticks to Minkowski space, I’m hoping to work on writing something about the relation to Euclidean space.
• There’s an interview with Nima Arkani-Hamed here. His talk at the recent PASCOS 2017 conference (real title is second slide “What the Hell is Going On?”) gives his take on the current state of HEP, post failure of the LHC to find SUSY. He’s sticking with his 2004 “Split SUSY” as his “Best Bet”. I’d like to think his inspirational ending claiming that the negative LHC results are forcing people to rethink the foundations of the subject, asking again the question “What is QFT?” reflects reality, but not sure I see much of that.
• This year’s LHC startup has been going well, with a new luminosity record already set, and 6 inverse fb of data already collected. For more, see here.
• Remember that “dark flow” that was supposed to be in the CMB data and evidence for the multiverse (see here)? Still not there, according to Planck (via Will Kinney).

Update: I’m sorry to hear the news of the untimely death of Maryam Mirzakhani, who was the first woman to win a Fields medal, awarded at the last ICM in 2014. Her work was described in detail at the time in this article by Curt McMullen.