Lieven Le Bruyn has relaunched his weblog under the new name Moonshine Math. The planned focus is monstrous moonshine.
Lieven converted some of the posts from the blog’s former life to PDF. You can find a links to the listings here.
Author Archives: Walt
Imposter!
Via Scott Aaronson and Peter Woit, I learn the story of Elizabeth Okazaki, who apparently has been hanging around the Stanford physics department for the past four years posing as a visiting scholar working on an interdisciplinary project. She has also apparently been using office space and even sleeping in the building. The range of reactions I’ve seen have been from shock and fear to pity, to amusement, but I haven’t seen anyone express my reaction: admiration. Assuming, as many people have suggested, that Okazaki is someone down on her luck looking for a place to stay, I have to admire her ingenuity in solving her problem. Physics departments have a high tolerance for personal idiosyncracy, and someone who keeps weird hours would never stand out in one. Physicists are a little vague on they do in humanities departments, so sprinkle a little interdisciplinarity on your project, and presto!, instant credibility. Her whole plan was practically scientifically designed to succeed for years. Maybe the NSF should give her a grant.
Stanford had another case of an interloper which in some ways is even more interesting. Azia Kim actually moved into the dorms and successfully posed as a college student for eight months. Okazaki’s plan only required the ingenuity of coming up with the cover story, and then sticking to it. Kim had to actually pretend to take classes to keep up her pretense. She also had to sneak into the dining halls to eat, and to climb back up into her dorm room window every night. I can’t even imagine the chutzpah it took to trick her way into dorm room, knowing how easy it would have been for her to get caught. It all required considerable courage.
Rumors of the abc conjecture
In late May, Peter Woit posted that Lucien Szpiro had announced a proof of the abc conjecture at the Goldfeld conference. In comments here, commenter Z passes along a rumor (with emphasis on rumor) that Szpiro’s proof has a significant flaw. Peter has updated his post to mention he’s hearing similar things.
Peter links to a couple of resources on the conjecture, which implies several other results (including most famously Fermat’s Last Theorem): The abc conjecture home page, and a survey article by Dorian Goldfeld.
Tenth Carnival of Mathematics
The tenth Carnival of Mathematics is up at Math Notations. The next carnival will appear at Grey Matters.
Maskin and Roberts on General Equilibrium
I was doing some more reading on general equilibrium, when I came across On the Fundamental Theorems of General Equilibrium by Maskin and Roberts, which gives a succinct proof of the existence of general equilibrium, as well as the two subsidiary results known as the first and second welfare theorems. It’s particuarly good in spelling out the mathematical relationship between the different results. (Be warned, though. It’s completely unintelligible if you don’t have a separate description of the model handy, though.)
I found the paper via this post by Michael Greinecker on his weblog Yet Another Sheep.
Elsevier Ends Arms Fairs
Elsevier, one of the major commercial academic publishers, had the curious side business of hosting arms fairs. After pressure from customers and authors, they have decided to exit the business.
Via Crooked Timber.
Final Word on “Latest Paper on ArXiv”
Bernhard Krötz has added another update on Tribikram Pati’s preprint. He now reports that the paper does not in fact disprove the Riemann hypothesis. Details provided by a colleague.
Ninth Carnival of Mathematics
The ninth Carnival of Mathematics is up at JD2718. It’s shockingly alphabetical for a collection of math posts.
Mathematical Complexity of Simple Economics
I ran across an old article by Donald Saari from the Notices of the AMS,
Mathematical Complexity of Simple Economics, which explains how some simple models of the economy can have arbitrarily complicated dynamics.
The basic model in economics of the economy as a whole is that of general equilibrium (GE). General equilibrium is a model of the economy where goods are traded for money which are traded for goods. It’s assumed that all of the goods are used up, and no one has money left over; prices are assumed to take on a value such that both of these things occur. It’s also assumed that in equilibrium the supply and demand of each good are exactly equal: everyone who wants to buy or sell at the current price is able to. The implicit dynamical idea is that if demand exceeds supply, then prices will go up, and if supply exceeds demand prices will go down. In this model, markets as said to clear.
It’s not easy to show that such market-clearing prices even exist. Under certain convexity assumptions, they can be shown to exist using the Brouwer fixed point theorem. The model, as stated, has no dynamics: prices achieve their equilibrium values, and that’s where the story ends. But as I mentioned above, there is an implicit dynamic story that whenever prices are too high, they adjust downwards, and when they are too low, they adjust upwards.
Saari’s article is about the difficulties that arise when taking that model of dynamics seriously. Assuming that prices adjust in proportion to how far supply and demand are apart can lead to arbitrarily complicated dynamics, even chaotic dynamics.
Real Reductive Groups
John Armstrong has written an overview of the representation theory of real reductive groups, based on a series of lectures by Gregg Zuckerman. The focus is providing enough background to understand the significance of the Atlas of Lie Group’s highly touted announcement. I particularly recommend the first post as a whirlwind introduction to the theory: