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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 8th 2019

Preprint today by Yau et al., relating $p$-adic strings to the Riemann zeta function:

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 8th 2019

added more references. Should add some pointer to Bruhat-Tits trees. But no time now.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeJan 9th 2019

So this is developing the open bosonic corner you mention in the penultimate paragraph of your MO question?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 9th 2019

Yes.

It sounds rather striking what they say about Riemann zeta zeros corresponding to the adelic string spectrum. But I haven’t had time yet to try to absorb it.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeJan 9th 2019

Yes, quite something if some aspect of the Riemann hypothesis emerges from one corner of a “more general number theoretic and homotopy-theoretic refinement of string scattering amplitudes”.

Is there anything deep in mathematics not touched by string/M-theory?

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJan 10th 2019
• (edited Jan 10th 2019)

One thing I haven’t appreciated before is how a Bruhat-Tits building here serves as the disk-shaped worldsheet of the open string.

I have no idea how this relates to taking elliptic curves over arbitrary rings as closed string vacuum diagrams, as it happens in the construction of the string orientation of tmf.

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeJan 10th 2019
• (edited Jan 10th 2019)

To associate some fog with more fog, I wonder if topological Langlands is about here, relating arithmetic to homotopy theory. I see it gets a mention in Eric Peterson’s new book Formal Geometry and Bordism Operations footnote 18, p. 361.

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJan 29th 2020

added this pointer on the suggestion that the disk worldsheet of the open p-adic string is to be identified with the Bruhat-Tits tree $T_p$: