The Defense Department has awarded a $7.5 million grant to Steve Awodey of CMU, Vladimir Voevodsky of the IAS and others to support research in Homotopy Type Theory and the foundations of mathematics. I had thought that getting DARPA 10 years ago to spend a few million on Geometric Langlands research was an impressive feat of redirection of military spending to abstract math, but this is even more so.
On some kind of opposite end of the spectrum of government spending on mathematics, there’s the story of the NSA, the largest employer of mathematicians in the US. Tom Leinster has an article in New Scientist about the ethical issues involved. More at the n-category cafe.
Seven years after the NSA-backdoored NIST standard was discovered by Microsoft researchers, and seven months after Snowden documents confirmed this (see here), the NIST has now removed the backdoored standard from its random number generator standards. As far as I know there has never been an explanation from the NIST explaining how the backdoored algorithm was made a standard, or why anyone should trust any of the rest of their cryptographic standards at this point. Earlier in the year they issued a Draft report on their standards development process which explained nothing about what had happened. The language about the NSA in the report is:
NIST works closely with the NSA in the development of cryptographic standards. This is done because of the NSA’s vast expertise in cryptography and because NIST, under the Federal Information Security Management Act of 2002, is statutorily required to consult with the NSA on standards.
which seems to indicate they have no intention of doing anything about the problem of NSA backdoors.
On the Langlands front, for those who don’t read French Vincent Lafforgue has produced an English translation of the summary version of his recent summary of his recent work on global Langlands for function fields (already proved by his brother, but he has a way of doing things without using the trace formula).
Langlands continues to add material to his web-site at the IAS. See for instance his long commentary on some history at the end of this section and his recent letter to Sarnak with commentary at the end of this section, where he gives his point of view on the state of the understanding of functoriality and reciprocity.
Sabine Hossenfelder has some interesting commentary on her experiences in the academic theoretical physics environment here.
Mark Hannam has some related commentary on academia at his new blog here.
I’m still trying to finish a first draft of notes about quantum mechanics and representation theory (available here). I recently came across some similar notes which are quite good by Bernard, Laszlo and Renard.
David Renard also has here some valuable notes on Dirac operators and representation theory.
Last Friday and Saturday at the University of South Carolina there was a Philosophy of the LHC Workshop, with talks here. Many of the talks were about the nature of the evidence for the Higgs and its statistical significance. James Wells talked about the supposed Higgs naturalness problem. He argues (see paper here) that you can’t base the problem on the Planck scale and quantum gravity since you don’t know what quantum gravity is (I strongly agree…). Where he loses me is with an argument that there must be lots more scalars out there than the Higgs (because string theory says so, or it just doesn’t seem right for there to only be one), and these cause a naturalness problem. Of course, once you have the naturalness problem, SUSY is invoked as the only known good way to solve it.