Author Archives: Walt

Press Release from Yau’s Lawyer

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Did anyone else recieve a press release from Shing-Tung Yau’s lawyer? With no explanation, I was sent this press release from Howard Cooper, Yau’s lawyer, denying the version of events described in Nasar and Gruber’s New Yorker article, Manifold Destiny. There’s nothing in the e-mail, other than press release, so as far as I know they either a) sent it to me because I linked to the New Yorker article, b) sent it to everyone with an e-mail address on this site, or c) everyone in the world. (In fact, I almost deleted the mail as spam without reading it.)

The web version of the press release links to this letter from Cooper to the article’s authors, detailing their specific charges. The letter is careful to make it sound like they could sue, but they haven’t made up their mind to do so yet.

Sunspot Equilibria

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A sunspot equilibrium is a market equilibrium in which prices depend on otherwise irrelevant random variable. The name is inspired by a theory of nineteenth century economist William Jevons that sunspots affected the stock market. (The theory, while wrong, isn’t quite as rediculous as it sounds. Jevons thought, by looking at the data he had on sunspots and agricultural prices, that he detected a pattern that indicated that sunspots caused crops to fail, which in turn caused recessions.)

A sunspot equilibrium would then be a self-fulfilling prophecy. If everyone expected that sunspots caused recessions, that in principle could be sufficient to cause a recession, even if the cause-and-effect existed entirely in people’s heads. Note that this outcome, while not optimal, would still be individually rational: even if you knew that sunspots didn’t really cause recessions, you would know that everyone else was expecting a recession, so you would act accordingly.

Karl Shell, one of the inventors of the concept, has a list of links to his papers on sunspot equilibria. In particular, he links to a short survey article he co-authored with Bruce Smith.

Hidden Subgroup Problem

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Interestingly, known public-key cryptosystems all seem to depend on the difficulty of the hidden subgroup problem. Suppose you have a group that can observe, and a subgroup that you cannot observe. Instead, you have a function that is constant along cosets of the group and different for different subgroups. The hidden subgroup problem is to compute a generating set for the subgroup just by evaluating the function. The problem generalizes integer factorization, the graph isomorphism problem and the problem of finding the shortest vector in a lattice. An efficient algorithm would apparently crack all known public-key cryptosystems.

Chris Lamont has a survey paper on the hidden subgroup problem in quantum computing, one that does not assume any background in quantum mechanics. Dave Bacon has some thoughts on an alternate approach.

Lattice Cryptography

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I was under the impression that the uncracked public-key cryptosystems were all based on number theory, which made them vulnerable to variants of Shor’s algorithm. Yesterday I learned via Dave Bacon that there are cryptosystems based on the hardness of finding the shortest vector on a lattice. Here is a survey paper on the subject by Oded Regev. There is also the McEliece cryptosystem, which is based on coding theory.

September Notices

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I finally had a chance to take a look at the September Notices of the AMS. Allyn Jackson’s Conjectures No More summarizes the conventional wisdom that the Poincaré and Geometrization conjectures are now theorems. What is… a quasicrystal?, by Marjorie Senechal, describes quasicrystals (crystals whose diffraction pattern implies they have symmetries that cannot be explained by a cyrstallographic group) and Penrose tilings.

The feature article, Notes on the Deuring-Heilbronn Phenomenon, by Jeffrey Stopple, discusses some results on Dirichlet L-functions.

Back from Vacation and Open Access

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I’m back from vacation. With any luck, I’ll even think of something to say. Until that happens, I wanted to link to Peter Woit’s post, Open Access Publishing, which links to this CERN task force report on the subject. I haven’t read the report, but Peter’s description makes it sound pathetically timid. As he characterizes it:

The CERN task force doesn’t seem to me to be providing a viable long-term plan for moving to the kind of open access model they are supporting. It doesn’t address the fundamental problem of keeping a system where physicists hand over the scientific literature to Elsevier, then have to figure out how to buy it back.