Secret Blogging Seminar

I’d been meaning to write a plug for my paper A self-dual integral form for the moonshine module on this blog for almost 7 years, but never got around to it until now. It turns out that sometimes, if you wait long enough, someone else will do your work for you. In this case, I recently noticed that Lieven Le Bruyn wrote up a nice summary of the result in 2021. I thought I’d add a little history o…

A few weeks ago, I e-mailed Will Sawin excitedly to tell him that I could extend the new bounds on three-term arithmetic progression free subsets of to . Will politely told me that I was the third team to get there — he and Eric Naslund already had the result, as did Fedor Petrov. But I think there might be some expository benefit in writing up the three arguments, to see how they are all really …

There seems to be a rule that all progress on the cap set problem should be announced on blogs, so let me continue the tradition. Robert Kleinberg, Will Sawin and I have found the rate of growth of three-colored sum-free subsets of , as . We just don’t know it is that what we’ve found! The preprint is here. Let me first explain the problem. Let be an abelian group. A subset of is said to be free …

It is far from clear to me that Springer’s copyright agreement (quoted below) is compatible with posting your paper on the arXiv under the CC-BY license. Happily, a Springer representative has just confirmed for me that this is allowed: Let me first say that the cc-by-0 license is no problem at all as it allows […]

Here is a fun problem, with a great story and a surprising answer. According to the Talmud, in order for the Sanhedrin to sentence a man to death, the majority of them must agree to it. However R. Kahana said: If the Sanhedrin unanimously find [the accused] guilty, he is acquitted. (Babylonian Talmud, Tractate Sanhedrin, […]

Back in graduate school, I read a beautiful paper of Kenyon, Okounkov and Sheffield. It started with the following physical story. This is the corner of a crystal of salt, as seen under an electron microscope. (I took the image from here, unfortunately I couldn’t find better information about the sourcing.) As you can see, […]

We’ve just posted an ad for up to 3 continuing positions at the Mathematical Sciences Institute, at the Australian National University, in Canberra. (Where I work!) It’s up on mathjobs, but applicants will need to apply through the university website. Here’s the pitch: The Mathematical Sciences Institute at the Australian National University is seeking to […]

In this post we will give a heuristic derivation of a result of Vershik, describing the shape of a random partition of a large integer . (Vershik’s Russian original is available here; English translation is pay-walled.) By a partition of , we mean positive integers with . We draw a partition as a collection of […]

I’d like to make another attempt at a topic I handled badly before: How Legendre duality shows up in statistical mechanics (or, at least, toy models thereof). We are going to be considering systems with parts, and asking how many states they can be in. The answers will be exponential in , and all that […]

It is a minor spoiler to say why mathematicians will enjoy this story by Scott Alexander but I predict many of you will.

Update — there are now not one, but two, positions available! The application has been extended to the end of November. We’ve just put up an ad for a new 2 year postdoctoral position at the ANU, to work with myself and Tony Licata. We’re looking for someone who’s interested in operator algebras, quantum topology, […]

Those of you who are interested in college math instruction may be interested in a no-longer-so-new blog “Michigan Math In Action”, which a number of our faculty started last year. (I was involved in the sense of telling people “blogs are fun!”, but haven’t written anything for them yet.) It mostly features thoughtful pieces on […]

Just a quick reminder that, if you are looking for graduate support to attend ALGECOM at the University of Michigan on Saturday October 24, or to register for the poster session, you should please send an e-mail to speyer@umich.edu by Tuesday Sept 15. (Yes, after sunset but before midnight is fine, I won’t be online […]

Let be a finite group, and let be a positive integer dividing . Then the number of solutions to in is divisible by . This is a 1907 theorem of Frobenius. Along with the Sylow theorems, it is one of the few nontrivial elementary results about a completely general finite group. And it has some […]

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 […]

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 speakers, namely, Jonah Blasiak (Drexel University) Laura Escobar (University of Illinois at Urbana-Champaign) Joel Kamnitzer (University of Toronto) Tri Lai (IMA and University of […]

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 […]

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 […]

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 […]

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. […]