A collection of links to round out the year:
- The Seminaire Bourbaki talks this January look unusually interesting. Luckily I’ll be in Paris at that time.
- For an end of year present, Jacob Lurie has posted a version of his unfinished next book, Spectral Algebraic Geometry. It’s advertised as much more user-friendly than previous versions of the same material and that’s quite true after reading the first chapter.
- If 850 pages or so of this sort of thing isn’t enough to keep you busy during the break between terms, try Lurie’s Harvard colleague Dennis Gaitsgory’s A study in derived algebraic geometry, a book project with Rozenblyum, also in a preliminary version (around 1100 pages), with more to come. I’m hoping for the more user-friendly version of this one…
- Also from Harvard, videos of last month’s Current Developments in Mathematics talks are now available here. At least the first of Peter Scholze’s talks is rather user-friendly.
- Very, very user-friendly (especially if you read Japanese) are the Japanese television versions of Edward Frenkel’s talks earlier this year at MSRI, available here.
- If you just can’t get enough of the new 750 GeV particle, you probably should read Tommaso Dorigo’s take on it.
- Back when I was writing about the AMS’s role as a mouthpiece for the NSA in its attempts to mislead people about their role in backdooring an NIST crypto standard (see here and here), one thought I kept in mind was that since this standard supposedly was never used in anything important, maybe one shouldn’t get so upset. Recent news (see Matthew Green for an explanation) is that this bad crypto actually was used in something quite important: widely used firewall/VPN hardware from Juniper Networks. Quite likely this was used by the NSA to get access to much of the traffic on a wide variety of networks.
The story is actually much more complicated than one can believe, with a still unclear sequence of changes in the software indicating that others, possibly a foreign government, took advantage of the NSA backdoor to compromise these systems. Green points out that this makes very clear the problem with government-mandated backdoors: even if you trust the government, they make it much easier for others to take advantage of the security problems they have introduced:
One of the most serious concerns we raise during these meetings is the possibility that encryption backdoors could be subverted. Specifically, that a backdoor intended for law enforcement could somehow become a backdoor for people who we don’t trust to read our messages. Normally when we talk about this, we’re concerned about failures in storage of things like escrow keys. What this Juniper vulnerability illustrates is that the danger is much broader and more serious than that.
The problem with cryptographic backdoors isn’t that they’re the only way that an attacker can break into our cryptographic systems. It’s merely that they’re one of the best. They take care of the hard work, the laying of plumbing and electrical wiring, so attackers can simply walk in and change the drapes.
- If you just can’t get enough of my and other people’s views on string theory, Ben Winterhalter has a piece on the Jstor blog, telling the story of his attempts to figure out what’s going on with extra dimensions.
- Among the many great articles at Quanta, I can recommend this one, which features my Columbia colleague Wei Zhang.
Happy New Year!