There aren’t many blog posts about vertex operator algebras, so I thought I’d help fill this gap by mentioning a substantial advance by Jethro van Ekeren, Sven Möller, and Nils Scheithauer that appeared on the ArXiv last month. The most important feature is that this paper resolves several folklore conjectures that have been around since near the beginning of vertex operator algebra theory. This was good for me, since I was able to use some of these results to prove the Generalized Moonshine Conjecture much more quickly than I had expected. I won’t say much about moonshine here, as I think it deserves its own post.
The University of Michigan at Ann Arbor is proud to be hosting
ALGECOM, the twice annual midwestern conference on algebra, geometry
and combinatorics on Saturday, October 24. We will feature four
Jonah Blasiak (Drexel University)
Laura Escobar (University of Illinois at Urbana-Champaign)
Joel Kamnitzer (University of Toronto)
Tri Lai (IMA and University of Minnesota)
as well as a poster session. If you would like to submit a poster, please e-mail (David Speyer) with a quick summary of your work by September 15.
This conference is supported by a conference grant form the NSF. Limited funds are available for graduate student travel to the conference. Please contact (David Speyer) to request support, and include a note from your adviser.
More information will be added to our website as it becomes available.
We hope to see you there!
A number of blogs I read are arguing about a paradox, posed by tumblr blogger perversesheaf. Here is my attempt to explain what the paradox says.
Suppose that a drug company wishes to create evidence that a drug is beneficial, when in fact its effect is completely random. To be concrete, we’ll say that the drug has either positive or negative effect for each patient, each with probability . The drug company commits in advance that they will state exactly what their procedure will be, including their procedure for when to stop tasks, and that they will release all of their data. Nonetheless, they can guarantee that a Bayesian analyst with a somewhat reasonable prior will come to hold a strong belief that the drug does some good. Below the fold, I’ll explain how they do this, and think about whether I care.
Amnon Neeman has just put up an ad for two postdoctoral positions at the ANU. He says: “The successful applicants should have strong research interests and activities in or related to one of the following fields: Algebraic Geometry, Commutative Algebra, Representation Theory, Algebraic Topology, Algebraic K-Theory. Skills at applying the techniques of triangulated categories to these areas would be a plus.”
These are excellent positions — available for up to 3 years, with no teaching requirements, and salaries in the AUD81-89k range.
Applications close at the end of January, and I hear Amnon is keen to hire as soon as possible.
Text of the announcement below:
Dear Colleagues,We the undersigned announce that, as of today 15 September 2014, we’re starting an indefinite strike. We will decline all papers submitted to us at the Journal of K-Theory.Our demand is that, as promised in 2007-08, Bak’s family company (ISOPP) hand over the ownership of the journal to the K-Theory Foundation (KTF). The handover must be unconditional, free of charge and cover all the back issues.The remaining editors are cordially invited to join us.Yours Sincerely,Paul Balmer, Spencer Bloch, Gunnar Carlsson, Guillermo Cortinas, Eric Friedlander, Max Karoubi, Gennadi Kasparov, Alexander Merkurjev, Amnon Neeman, Jonathan Rosenberg, Marco Schlichting, Andrei Suslin, Vladimir Voevodsky, Charles Weibel, Guoliang Yu
This is a post I’d been meaning to write for several years, but I was finally prompted to action after talking to some confused physicists. The Monster Lie Algebra, as a Lie algebra, has very little structure – it (or rather, its positive subalgebra) is quite close to being free on countably infinitely many generators. In addition to its Lie algebra structure, it has a faithful action of the monster simple group by Lie algebra automorphisms. However, the bare fact that the monster acts faithfully on the Lie algebra by diagram automorphisms is not very interesting: the almost-freeness means that the diagram automorphism group is more or less the direct product of a sequence of general linear groups of unbounded rank, and the monster embeds in any such group very easily.
The first interesting property of the Monster Lie Algebra has nothing to do with the monster simple group. Instead, the particular arrangement of generators illustrates a remarkable property of the modular J-function.
The more impressive property is a *particular* action of the monster that arises functorially from a string-theoretic construction of the Lie algebra. This action is useful in Borcherds’s proof of the Monstrous Moonshine conjecture, as I mentioned near the end of a previous post, and this usefulness is because the action satisfies a strong compatibility condition that relates the module structures of different root spaces.
I’ve just got back from talking to Roxanne Missingham, the University Librarian here at ANU, about Elsevier, and I want to quickly report on what I learnt.
I don’t yet have any of the juicy numbers revealing what libraries are paying for their Elsevier subscriptions (as Timothy Gowers has been doing in the UK; if you haven’t read his post do that first!). Nevertheless there are some interesting details.
Essentially all the Australian universities, excepting a few tiny private institutes, subscribe to the Freedom collection (this is the same bundle that nearly everyone is forced into subscribing to). The contracts are negotiated by CAUL (the Council of Australian University Librarians).
My librarian was very frank about Article Processing Charges (APCs) constituting double-dipping, whatever it is that Elsevier and the other publishers say. The pricing of journal bundles is so opaque, and to the extent we understand it primarily based on the historical contingencies of print subscription levels more than a decade ago, that in practice the fraction of articles in a subscription bundle for which APCs have been paid has no meaningful effect on the prices libraries pay for their bundles.
I think this point needs wider dissemination amongst mathematicians — whatever our complaints about APCs inhibiting access to journals for mathematicians without substantial funding, we are just plain and simple being ripped off. Gold open access hybrid journals are a scam.
Now, on to some details about contracts. First, my librarian confirmed the impression from Gowers’ investigations in the UK — bundle pricing is based largely on historical spending on print subscriptions, with annual price increases. Adding some interesting context on the numbers we’re now seeing out of the UK, she told me that the UK is widely perceived as having received a (relatively) great deal from Elsevier, in terms of annual price increases. If the UK numbers scared you, be aware that here in Australia we may well have it worse. A curious anecdote about historical pricing of subscriptions is that one division of CSIRO happened to have cancelled most of their print journals the year before they took out an electronic subscription with a commercial publisher, and as a result got an excellent deal. The Australian universities have apparently mostly signed confidentiality agreements regarding their journal subscription costs (as we expect, by now), but my understanding of the conversation was that the ANU in particular had not.
Finally, my librarian pointed out that doing what I hope to do next, namely use the FOI act to obtain detailed information on Elsevier subscription costs, may be counterproductive, as the most likely result of unusual discrepancies in pricing being revealed is some libraries simply having budgets cut, rather than actually giving the negotiators any more power in the future. I got the impression she’d talked to other Australian librarians about this, and there was some amount of nervousness.
I’ve been told I should go talk to Andrew Wells, the librarian at UNSW, and after posting this I’m going to get in touch with him!
In algebraic geometry, we like to make statements like: “two conics meet at points”, “a degree four plane curve has bitangents”, “given four lines in three space, there are lines that meet all of them”. In each of these, we are saying that, as some parameter (the conics, the degree four curve, the lines) changes, the number of solutions to some equation stays constant. The “principle of conservation of number” refers to various theorems which make this precise.
In my experience, students in algebraic geometry tend to pick up the rough idea but remain hazy on the details, most likely because there are many different ways to make these details precise. I decided to try and write down all the basic results I could think of along these lines.
This June 8 to 14, there will be a week long gathering in Snowbird, Utah for young mathematicians working on cluster algebras. The target audience here are either current graduate students, or people with Ph. D. in the last 3 or so years, who would be ready to start working on problems in cluster algebras. The hope is to spend a lot of time getting collaborations and projects going during the week. The organizers are Michael Gekhtman, Mark Gross, Gregg Musiker, Gordana Todorov and me.
We still have room for a number more applicants, so we would like to encourage more of you to apply. Please note that the application deadline of March 1 is firm.