Farey fractions, Ford circles, and SL_2. October 18, 2011
Posted by Scott Carnahan in group theory, Number theory.12 comments
The topic of this post came up during a conversation with some physicists about the fractional quantum Hall effect (which is quite fascinating, but I don’t feel particularly qualified to discuss). I have decided to set it down here in the hope that, as long as I have an internet-capable device with me, I won’t have to rederive it in front of people again. Some of this material appears in Apostol’s Modular functions and Dirichlet series in number theory and Conway’s The sensual form. I’d be happy to hear about other good treatments.
The many disguises of rhombus tilings October 17, 2011
Posted by David Speyer in Uncategorized.2 comments
For a while now, I thought I should write up a blog post on the many different combinatorial objects which are in bijection with rhombus tilings of centrally symmetric polygons: various constructions with reduced words, oriented matroids, projections of hypercubes, strongly separated sets and so forth. But I kept putting it off because I knew it would take a long time to write correctly, with all the motivation and lots of figures it deserved.
Yesterday I had a very nice conversation about rhombus tilings with Lionel Levine, and I decided it was time to consolidate my knowledge and fill in the gaps. So I sat down and dumped everything I could think of into a question on MO. Note that this is a question and even a community wiki one — if you know of more results to add, please head over there and add them!
Reflecting on the sociology of mathematics, it seems to me that we are seeing a growth in ways to do a quick and sloppy job publishing something. Fifteen years ago, this would have been a survey article that would have taken weeks for me to research and edit. Five years ago, this would have been a blog post written over several days. Now I’ve written something much less polished, but I was able to do it in an evening in between taking care of my baby. I’m not sure whether it’s good or bad, but it seems to have been the only way I could get this written at all.
The NSF and career-life balance October 9, 2011
Posted by Noah Snyder in math life, NSF madness, WANT.3 comments
The NSF recently announced some new policies concerning work-life balance. There seems to have been a publicity push about it on the part of the White House, as it made the regular news. The main changes seem to be adding flexibility to grant rules for new parents. Mostly pretty obvious stuff like letting people delay the use of their grant if they go on parental leave. Good ideas to be sure, but mostly just catching up to what they already should have been doing.
This reminded me of one of my favorite ideas I’ve heard for an NSF policy change which would help career-life balance. Currently the MSPRF postdoc policy reads:
Changes in the host institution will be approved only under extremely unusual and compelling circumstances… Securing a position at an institution other than the proposed host institution is not considered an “extremely unusual and compelling circumstance.”
The suggestion is to change this by adding the line:
Nonetheless, if the fellow has a partner who is unable to procure a job near the sponsoring institution, and both the fellow and their partner have job offers in other city, that will be considered compelling circumstances.
Things learned today in calculus class October 5, 2011
Posted by David Speyer in Uncategorized.2 comments
Usain Bolt can accelerate at 
For anyone who is going to be teaching about computing derivatives numerically, my students really enjoyed looking at the data in this paper. (I give them just a scan of table 1, and have them do the analysis themselves.)
Any other great data sources?
Subfactors of index less than 5 October 4, 2011
Posted by Noah Snyder in Uncategorized.9 comments
Masaki Izumi, Vaughan Jones, Scott Morrison and I recently uploaded to the arXiv the 3rd and final part of the four part series “Subfactors of index less than 5.” This is a project we’ve been working on for a long time (since Emily, Scott and I started running Planar Algebra Programming Camps in spring of ’08), and after three years and a lot of work from many people it’s very exciting to finally have made it there.
In this post I’ll state the main theorem, say a few words about the history, and then explain the main takeaway lesson we learned in this project.
Employment opportunities October 3, 2011
Posted by Ben Webster in jobs.13 comments
Since we’ve already set the precedent that it’s OK to use the blog for job announcements, let me do a little promotion. My current home, Northeastern, has just posted postdoctoral and tenure-track job announcements. If people have questions about either position or life at NU, they are encouraged to email me (though there is a decent chance I’ll just refer you on to the appropriate authorities).
I particularly want to push the postdoctoral position, because, well, first of all I want to have a more talented postdocs around the department (more in number, no insult intended to our current postdocs); I’m also on the search committee for the position, so I have some responsibility to my colleagues to find good people to hire.
Furthermore, as we’ve discussed, titles for postdoctoral jobs are generally confusing; what exactly does “Research Instructor” mean? This is going to sound stupid, but it’s right there in the name; you’re supposed to do research and instruct people. We’re looking for people who will do both of those things well. Candidates are expected to be part of the research life of the department, and we are definitely hoping to find people whose interests overlap with faculty members here. We also take the teaching component of the job very seriously, but the teaching load is intended so that you have time to teach your classes well and work on other things; it is below Noah’s magic line at 3 semester courses a year.
Which is all a long way of saying I look forward to seeing your applications.
Random partitions I October 2, 2011
Posted by David Speyer in Uncategorized.8 comments
With trepidation, I am attempting to start another series of mathematical blog posts. The goal of this one will be to present random partitions as a toy model for thinking about random dimer configurations. Ideally, these posts will help prepare the reader to take on the ground breaking papers of Kenyon and Okounkov.
I say ideally because I have an infant daughter at home — her name is Josephine, she is adorable and demanding — so the installments of this series may be spaced very far apart. I make no plans to apologize for this. But I’ve been feeling the lack of mathematical blogging the last few months, so I’m giving it a shot.
The motivating question for today’s post will be: For 
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The mathematical internet is a great opportunity to promote yourself, but be polite! October 2, 2011
Posted by David Speyer in Uncategorized.Tags: planetMO
20 comments
I just posted this over on a discussion thread at meta.MO, and I thought it might deserve more visibility.
We’ve had some questions on meta.MO about how undergraduates applying to graduate school should view a presence on Mathoverflow, math.SE or in the math blogosphere. I was on the graduate admissions committee for the University of Michigan last year so, for what it is worth, here is my take:
