Yet More Math and Physics Items

Various items that may be of interest:

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).

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11 Responses to Yet More Math and Physics Items

  1. Peter Orland says:

    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.

  2. Peter Orland says:

    … and I guess I did not know before that his father was also someone whose papers (on Sobolev inequalities) I had read.

  3. theoreticalminimum says:

    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.

  4. DKepler says:

    … although some might argue that medieval theology and theoretical physics have seen a convergence in recent years…


    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.

  5. Johan Smit says:

    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.

  6. jackjohnson says:

    @ John Smit, Not that there’s anything wrong with that?

  7. Johan Smit says:


    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.

  8. jackjohnson says:

    @ johan smit, fair enough, thanks!

  9. anonymous says:

    Kirti Joshi published a part 2 of his Arithmetic Teichmuller spaces paper:

  10. bertie says:

    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’?

  11. Peter Woit says:

    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.

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