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The dishonest stopping paradox
*May 10, 2015*

*Posted by David Speyer in Uncategorized.*

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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.

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ANU hiring postdocs
*November 19, 2014*

*Posted by Scott Morrison in Uncategorized.*

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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.

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Grothendieck 1928-2014
*November 13, 2014*

*Posted by Scott Morrison in Uncategorized.*

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Editorial board of “Journal of K-Theory” on strike, demanding Tony Bak hands over the journal to the K-Theory foundation.
*September 14, 2014*

*Posted by Scott Morrison in Uncategorized.*

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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

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What makes the Monster Lie Algebra special?
*May 26, 2014*

*Posted by Scott Carnahan in group theory, mathematical physics, representation theory.*

Tags: moonshine

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Tags: moonshine

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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.

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Elsevier in Australia
*May 21, 2014*

*Posted by Scott Morrison in elsevier, evil journals, publishing.*

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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!

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The many principles of conservation of number
*March 4, 2014*

*Posted by David Speyer in Uncategorized.*

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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.

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Mathematical Research Community on Cluster Algebras in Utah this summer
*February 26, 2014*

*Posted by David Speyer in Uncategorized.*

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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.

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Australian Research Council journal list
*February 24, 2014*

*Posted by Scott Morrison in Uncategorized.*

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(This post may only be of interest to Australian mathematicians; sorry!)

Summary:A number of mathematics journals (e.g. Quantum Topology, Forum of Mathematics Sigma and Pi, and probably many others), are not listed on the new official journal list in Australia. Please, help identify missing journals, and submit feedback via http://jacci.arc.gov.au/.

Every few years the Australian Research Council updates their “official list of journals”. One might wonder why it’s necessary to have such a list, but nevertheless it is there, and it is important that it is accurate because the research outputs of Australian mathematicians are essentially filtered by this list for various purposes.

There is a new draft list out, and the purpose of this post is to coordinate finding missing journals, and to ensure that interested mathematicians submit feedback before the deadline of March 15. Please note that while in the past this list included dubious rankings of journals, the current list is just meant to track all peer reviewed journals in each subject. Having a journal missing entirely means that some published papers will not be counted in measures of a department’s or university’s research output.

You can access the full list here, just journals marked as mathematics here, and just the journals marked a pure mathematics here. These are not the “official” lists, which you have to create an account (follow the instructions at http://www.arc.gov.au/era/current_consult.htm) to view, and even then only an Excel version is available. I hope that by making these mathematics specific lists available in a standard format, more mathematicians will take the time to look over the list.

Please look through the lists. If you see something missing, please comment here so we all know about it. In any case, please submit feedback via http://jacci.arc.gov.au/ (you’ll have to create an account first) recommending inclusion of the journals identified so far. Submitting a missing journal requires identifying an article published in it by an Australia author; feel free to add this information here as well if appropriate. (Thanks to Anthony Henderson for pointing out this detail!)

It is also possible to submit additional “FoR” (field of research) codes for journals on the list, and this may be of interest to people publishing cross-disciplinary research. Feel free to make suggestions along these line here too: the AustMS has been advised that “multiple responses, rather than a single AustMS one, will carry more weight on this aspect”.

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Course on categorical actions
*February 7, 2014*

*Posted by Ben Webster in Shamelss Self Promotion.*

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I have the excellent luck to be sending this semester in Paris, thanks to the Fondation Sciences Mathématiques de Paris. Part of the deal is that I’m giving a weekly course at the “graduate level” (though I think I have more professors than graduate students in the course) on higher representation theory. Also thanks to FSMP, the course is being videotaped and posted online; the first installment is up here. I’m also posting the videos and additional commentary on a WordPress site; if you have any questions, you can always ask them there (or here, but maybe it’s more germane there).