http://vlafforg.perso.math.cnrs.fr/files/beamer-ted.pdf

Btw, he gave a pretty good talk at ICM2018. Even I managed to understand a few words here and there (mostly “is” and “the”) 🙂

Video here:

https://www.youtube.com/watch?v=lD8jE3NK8fw

Slide set:

http://vlafforg.perso.math.cnrs.fr/files/beamer-chtoucas-ICM-adelique.pdf

http://vlafforg.perso.math.cnrs.fr/

He made one (to me) very striking claim, that the functoriality conjecture could be thought of as a quantization problem, how to pass from a classical system to a quantum system. Can an expert enlighten me on what exactly he was referring to here?

]]>I’d be interested to hear a better answer from someone more expert, but my understanding is that that many of the original questions about the number field case raised by Langlands still remain open, with new insights needed to make progress on them. On the other hand, many of the Langlands program conjectures about number fields have been proved, with a high point the Taylor-Wiles proof of modularity, and recent progress that of the last item. I don’t think though there’s any sensible metric on these questions which would allow one to assign percentage completion numbers.

Since the original work of Langlands there have been huge extensions of his original ideas, providing a much larger vision unifying different areas of mathematics, often with proofs, not just conjectures. In particular the geometric theory as far as I know was not originally in the picture. For the current take from Langlands on that, all you need is to be able to read Russian and Turkish…

]]>https://writing-guidelines.web.cern.ch/entries/inverse-femtobarn

]]>….One inverse femtobarn corresponds to approximately 100 trillion (10^12) proton-proton collisions.

….

Note: Do not use inverse femtobarn in the public section of the website where it can be avoided – it is unnecessarily technical. Convert to approximate numbers of collisions instead.