Various items that may be of interest:
- Robbert Dijkgraaf was sworn in a few days ago as Minister of Education, Culture and Science in the Dutch government. Unclear who if anyone is director of the IAS at the moment, but David Nirenberg will take on this position February 1. Nirenberg is currently a professor of medieval theology and director of the Divinity School at the University of Chicago. This will be the first time in thirty-five years that the IAS director has not been a mathematician or physicist (although some might argue that medieval theology and theoretical physics have seen a convergence in recent years…).
- Lieven Le Bruyn has a posting about Huawei’s new research center in Paris (and adds more here), which seems to have attracted multiple Fields medalists, with Laurent Lafforgue’s affiliation recently changing from IHES to Huawei. Lafforgue held the Huawei chair in algebraic geometry at the IHES, which now is in the market for a new Huawei chair in algebraic geometry. The head of Huawei has recently emphasized the importance to the company of “bringing in talent with ‘tall noses'”.
- An interesting way to keep track of hot topics in US theoretical HEP might be to watch the “white papers” starting to appear as part of the Snowmass 2021/2 exercise. Two examples now on the arXiv are a seven-author white paper on the Emergence of Spacetime and a three-author one on Celestial Holography. There will be a program on Celestial Holography at the PCTS in Princeton in a couple weeks.
- On the Mochizuki/abc front, Jordan Ellenberg on Twitter points to this recent preprint from Kirti Joshi. Joshi claims inspiration from the IUT papers, but writes in a much more conventional mathematical language, and makes no claims to prove abc or any other major new results in number theory. One might optimistically hope that his work would clarify the true significance of Mochizuki’s IUT work.
Update: A very recent relevant paper from Joshi is this. It contains a detailed comparison of his point of view with Mochizuki’s, but avoids taking any position on the controversial Corollary 3.12 claimed by Mochizuki.
Update: To clarify the above. In this paper (Theorem 10.1.1) Joshi proves his version of Mochizuki’s Corollary 3.12. But importantly (in that paper): Along with Theorem 10.1.1, there is a discussion of why Joshi’s version of Corollary 3.12 is different from Mochizuki’s version and notably why his version does not imply Mochizuki’s version (according to Joshi, the two versions work with two different ambient sets to compute the theta-values locus–Joshi’s version uses a natural ambient set his theory provides–and it is deeply tied to Fargues-Fontaine Theory).
I have no idea what sort of leader of the IAS Nirenberg will be, but in my highly uninformed opinion, he is a serious and interesting scholar. His book “Anti-Judaism” on a store shelf attracted my attention only by its seeming weird. I overruled my prejudices and leafed through it. Then I bought it and I read the thing in a day.
… and I guess I did not know before that his father was also someone whose papers (on Sobolev inequalities) I had read.
Maybe this could be of interest. Gallimard have published Grothendieck’s R&S in two volumes and a fiction presumably inspired by the story of Perelman.
… although some might argue that medieval theology and theoretical physics have seen a convergence in recent years…
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Yes, some might argue the convergence, but it is unfair to drag whole of ‘theoretical physics’ into this. String theory is the ‘only game in town’ – at least in this regard. Your own posts on top string theorists promoting multiverse demonstrate this very well.
Another physics item: David Tong published lecture notes for supersymmetric field theory, where he indicates that the primary reason for studying the topic is to understand quantum field theory better and find more connections to mathematics, rather than to find beyond standard model physics for which there is no evidence of.
https://www.damtp.cam.ac.uk/user/tong/susy.html
@ John Smit, Not that there’s anything wrong with that?
jackjohnson,
There is nothing wrong with any of this. It’s just more evidence of an ongoing paradigm shift in theoretical physics, where the connections to speculative beyond standard model physics gets de-emphasised (due to the lack of evidence for supersymmetry at the LHC) and the focus is turning towards theoretical quantum field theory and toy supersymmetric models. Ten years ago these lecture notes would probably have dedicated an entire chapter or two to supersymmetric extensions of the standard model like MSSM and possible phenomenology at the LHC.
String theory is headed in the same direction as well, with the focus turning away from trying to find a theory of quantum gravity or to unify all the forces, and instead studying toy string theory models (or really toy CFT models) and applying the results to other quantum field theories.
@ johan smit, fair enough, thanks!
Kirti Joshi published a part 2 of his Arithmetic Teichmuller spaces paper: https://arxiv.org/abs/2111.04890
So with the linked Kirti Joshi paper, he derives results analogous to the IUT stuff including a result ‘of the same form’ as Corollary 3.12 but I gather there is some problem getting bounds which are as tight as Mochizuki’s otherwise Joshi would just go ahead and prove ABC wouldn’t he? Joshi is exceedingly polite towards Mochizuki’s work. However, if Joshi’s analogous construction does everything that IUT does,with the single exception of proving ABC, wouldnt that look a little bit like a ‘nail in the coffin’?
bertie,
My understanding is that Joshi is making no claims one way or another about Mochizuki’s Corollary 3.12, in particular not claiming he knows how to prove (or disprove) it. Maybe it’s a true statement, maybe it’s not. One thing that remains the same is that no one can explain Mochizuki’s proof of the statement in a convincing way.