Various things that may be of interest, ordered from abstract math to concrete physics:
- Jacob Lurie is teaching a course this semester on Categorical Logic. Way back when I was a student at Harvard this is the kind of thing I would have found very exciting, much less convinced of that now.
- Talks from a workshop earlier this month on representation theory are available here.
- The Harvard Gazette has an article about a project to develop a “pictorial mathematical language” first proposed by Arthur Jaffe. The project has a website here. It is being funded by an offshoot of the Templeton Foundation I didn’t know about, the Templeton Religion Trust, with one of their grants, TRT0080: “Concerning the Mathematical Nature of the Universe”, described as “exploring whether or not the universe admits of a consistent description, or more generally, whether our universe [can] be described by mathematics?”. They’re advertising a postdoc position here.
- Adam Marsh has a wonderful book on Mathematics for Physics, especially from the geometrical point of view, with lots of detailed illustrations. It’s available from World Scientific here, or as a website here (there are also articles on the arXiv, here and here).
- There’s a new Leinweber Center for Theoretical Physics at the University of Michigan, funded by an $8 million grant from the Leinweber Foundation. Inaugural talk was Arkani-Hamed on The Future of Fundamental Physics.
- Each year recently there has been a Physics of the Universe Summit, described by some as involving “one of those glitterati Hollywood banquets”. Some years ago, the glitterati evidently were interested in particle physics, recently instead it is quantum computing and AI (see last year and this year). At this year’s glitterati banquet, a kidnapping of Kip Thorne occurred.
- Alex Dragt has a book about Lie methods, with applications to Accelerator physics. If you’re looking for detailed very explicit information about symplectic transformations, there is a wealth of such material in this book.
- I’m hearing a rumor (via an anonymous comment here) that HyperKamiokande has been denied funding. Can anyone confirm or deny?
The Hyperkamiokande website http://www.hyperk.org/ even has a movie on the project. Will it be able to measure neutrino masses?
If the project really focuses on testing GUT only, its proponents did themselves a bad favor, now that GUTs seem to contradict experiments. But if Hyperkamiokande could measure neutrino masses, it would be a different thing. That might be the last topic of particle physics about which we know very little. Neutrino masses are often given as 1 eV +/- 1 eV which is really a unsatisfactory state of affairs.
Update: The other English website of Hyperkamiokande is much more specific on its aims: http://www.hyper-k.org/en/physics.html
The results would give Japanese physics a huge boost, and put them at the forefront of the particle physics world. Let us hope that the rumors are wrong!
It would be a big news if HK will not be financed, but I would not know how to interpret it in the grand-scheme of future fundamental research. Such a decision will boost even more Fermilab’s plans for DUNE, which will be the only “definitive” neutrino experiment on the market. The ILC is also in bad shape in Japan and I was indeed surprised by their will to go ahead with ILC and HK at the same time..
Let’s wait some informed comment. Meanwhile I’ll try to ask to some HK colleagues.
Remember that the T2KK experiment is also being planned, with some redundancy to HK.
Quoted: “Jacob Lurie is teaching a course this semester on Categorical Logic. Way back when I was a student at Harvard this is the kind of thing I would have found very exciting, much less convinced of that now.”
It would be very interesting to know what are Your doubts, reservations or objections to this topic and the reasons for the change of interest. From what I can see from the web-page, it is essentially a course on “topos theory”.
As a student I was fascinated by trying to learn about more and more abstract mathematical constructs of greater and greater generality, later realized the danger with this is that you end up saying less and less about more and more, in the limit saying nothing about everything.
Lurie is a great mathematician, I’m curious to see what he does with this material.
The truth about HyperK is that the budget for 2018 was postponed, which will delay the project with respect to its original schedule. The same thing happened in the past with SuperK/T2K, it seems to be the way it works in Japan.
By the way, who is Adam Marsh?
Most of categorical logic is no more abstract than the material in a typical undergraduate algebra course (indeed, most of the proofs are easier). It’s just that this material is not on the usual undergrad main sequence, due to the sociological/historical accident that mathematicians tend to know very little formal logic (a self-perpetuating accident, for obvious reasons).
It’s a lovely subject, because it is just barely abstract enough to support numerous examples, a fact which is enormously useful to workaday computer scientists like me.
thanks for the reply.
I do understand Your point (generalizations often treat more “objects” at the price of “forgetting” some of their structure), but I am not sure that the process of mathematical abstraction consists in just this step. Allow me to make a short comparison between two examples of abstraction: 1) “monoids” generalize “groups” (forgetting the existence of inverses) exactly as You say. In this case the generalization is blind to the “extra structure” available in the more specific case. 2) every group is canonically a “groupoid with only one object” and “groupoids” are a vast generalization of “groups”. In this case, what happens is that the *extra structure* necessary to define a groupoid “trivializes” (and becomes essentially invisible) in the case of the more special case of usual groups.
This example is not only academical: in physics people usually *define* “symmetry” as a group (hence if something is not a group, it is not a symmetry), still groupoids (and more generally categories) capture some significant aspects of the intuitive idea of symmetry. Of course “what we are able to fish … depends on the kind of net that we are allowed to use to fish” and there is the clear danger of saying that “something” is not a fish because it is too small (or too big) to be captured in a specific net 🙂
Best Regards (and thanks for the always stimulating comments and links).