The Hoffman-Singleton graph and groupoids October 16, 2013Posted by David Speyer in Uncategorized.
The Hoffman-Singleton graph is the unique graph on vertices with the following property: Every vertex is of degree and, between any two vertices, there is either an edge or a path of length two, but not both. The Hoffman-Singleton graph has a large symmetry group — order — and there are many ways to describe it that emphasize different symmetry properties. Various constructions describe it in terms of the geometry of the affine plane , the projective space or just pure combinatorics. Here is one more that I noticed the other day when reading through the original Hoffman-Singleton paper. While turning it into a blogpost, I noticed that the same observation was made by Markus Junker in 2005.
Conference videos April 30, 2013Posted by Ben Webster in Uncategorized.
Well, from my perspective at least, the conference was a success. We all made it through in one piece, and no one got trapped on the subway. If any of you are looking for the videos of the talks, they can be downloaded from this page. That’s a only a temporary hosting solution, but at least they’re available for the moment.
More on shameless promotion April 23, 2013Posted by Ben Webster in Uncategorized.
As those of you who’ve scrolled down the page know, the conference I mentioned a few months ago (now sadly memorializing the life of Andrei Zelevinsky) is starting tomorrow. Of course, for those of you who don’t live in the Boston area, coming to conference isn’t an option unless you were already traveling today, but I do have a (somewhat belated) announcement. Assuming that the AV gods are kind and everything goes as planned, it should be possible to watch the talks live (of course, we’ll also make the videos available after the conference, in case you’re busy). The schedule is here; the talks start at 10am tomorrow.
New open access journal in algebraic geometry March 3, 2013Posted by David Speyer in Uncategorized.
I just received an e-mail announcing that Compositio has launched an Open Access journal entitled Algebraic Geometry. Their website is live and promises “Open access implies here that the electronic version of the journal is freely accessible and that there are no article processing charges for authors whatsoever. The printed version of the journal will be available at the end of the calendar year against printing costs.”
The editorial board looks great, including L. Caporaso, J. Ellenberg, D. Maulik and R. Pandharipande. They will definitely get my next algebraic geometry paper.
This is really good news. It’s seemed clear from the debates on journals of the last year that what is needed is for people and institutions of high reputation to commit to running open journals. Compositio, and the editors they have found, are top of the line. From a selfish perspective, what makes me really happy is that I didn’t wind up on the editorial board.
Good work, and good luck, to Algebraic Geometry.
UK Parliament seeking feedback on Open Access support January 15, 2013Posted by David Speyer in Uncategorized.
Last September, the UK parliament earmarked £10 Million pounds from the science budget to support open access scientific publishing. Earlier this week, the UK parliament announced that they are seeking feedback on this policy, including “how the Government should address the concerns raised by the scientific and publishing communities about the policy”. Details of how to submit comments are here. I don’t know much about UK politics, so I can’t give much advice about how to frame your response, but the deadline is this weekend (Jan 18) so it seems important to get the word out.
Note some bizarre statements in the comment submission guidelines: They want submissions in Word or, if Word is not acceptable, another editable electronic format; they specifically state not PDF. (<rant> Why, oh why has the world forgotten RTF? Or plain ASCII? Or HTML? I understand why most people don’t want to use LaTeX, but the way that the world acts as if Word is the most convenient format drives me nuts. </rant>) They also say “[s]ubmisions become the property of the Committee.” That’s a bizarrely vague statement from a committee discussion copyright policy. I assume they mean that you are implicitly granting them the right to publish it, but if I were phrasing that I would say “you retain copyright to your words but grant us permission to retain your file/manuscript and to publish…”.
I don’t think that the points in the preceding paragraph represent bad intent on the part of the committee, but I do think they show an ignorance of how things are done in the academic world. So let’s help them out!
A calculus free proof of the spectral theorem December 3, 2012Posted by David Speyer in Uncategorized.
Let be an real symmetric matrix. Let be an eigenvalue and be a corresponding eigenvector. Then
We deduce that . And is clearly a positive real, so .
This immediately shows that the characteristic polynomial of has only real roots.
Shameless conference promotion November 14, 2012Posted by Ben Webster in Uncategorized.
So, obviously posting on this blog has ebbed a little (I keep hoping to reverse this trend, but I think we’ve all found that demands on our time that come before blog posting tend to ratchet upward, not downward). I assume there are still a few people reading, though, and I wanted to do a little promotion.
One of the thing that’s been demanding my time lately has been conference organization. We’re planning a conference at Northeastern next spring in recognition of the 60th birthday of Andrei Zelevinsky, with the exteremely original name of “Algebra, Combinatorics and Representation Theory”. I think it’s going to be great, and I encourage any of you who are able and interested to attend; we have a really great line-up of speakers.
For more information, see our website. I want to particularly encourage young people to attend; we’re really hoping (cross your fingers) to have funding for grad students and postdocs. (Furthermore, it will help us to obtain said funding if young people express an interest in coming. So, if you would like to come, please register).
Rant to me about algebra books October 25, 2012Posted by David Speyer in Uncategorized.
Next term, I will be teaching the second semester of graduate algebra here at Michigan. The big mandatory topics are finite groups and Galois theory. There is usually time for a bit more of whatever the instructor wants to fit in. I want to do some representation theory. In my dreams, we’ll also do a bit of playing with number fields, but that might be overly ambitious.
My project for the next few weekends is to skim through as many algebra texts as I can and pick one to use. So I thought I’d put up a request for your opinions. Below the fold, some of my criteria:
What I’m reading October 24, 2012Posted by David Speyer in Uncategorized.
I haven’t had a long post for a while, but there is lots of great math on the internet. Here are some of the things I’m trying to find time to read.
Integrable systems, toric geometry and Okounkov bodies The answer to a question which many people have asked: What’s the relationship between integrable systems and torus actions? Allen Knutson has been telling people roughly what the picture should be for a while, but the details seemed very hairy; now they are all resolved. That gets us half way to the question I want to know the answer to: “What is the relation between these integrable systems and cluster algebras?”
A closed formula for the decomposition of tensor products of Specht modules for the symmetric group A positive formula for stable Kronecker coefficients! (Corollary 4.08) And a proof which relies on the sort of planar diagram philosophy that people on this blog love. Congratulations to Bowman, de Visscher and Orellana.
Causal diagrams and causal models Not new, but new to me. I had always learned that, if and are correlated, then the only way to tell which one causes which (or whether they are both caused by something else) was by a randomized trial. Not true! You can make this determination in a purely observational manner, by seeing how and both correlate with . Apparently, this was known since the late 80′s, but my stats course never covered it. Makes me want to go back and work in algebraic statistics.
And I’ll take the opportunity to plug a paper of my own which has been a long time coming. Schubert problems with respect to osculating flags of stable rational curves The Shapiro-Shapiro conjecture, now proved by Mukhin, Tarasov and Varchenko shows that any distinct points on give Schubert problems whose solutions are, astonishingly all real. What happens when the points collide? And what does this have to do with the work of Henriques and Kamnitzer?
It would be harmful to design all mathematical contests to be proctorable September 30, 2012Posted by David Speyer in Uncategorized.
This rant is inspired by a debate going on at meta.math.SE. The subject of the debate is what steps the moderators should take to prevent the use of math.SE to cheat in ongoing math competitions. If you have an interest in the subject and an account on meta.math.SE, I encourage you to head over and participate including, if you are so inclined, voting on the poll questions I just posted.
The particular point I want to address is posters who write that the fault is with contest organizers, for not designing their contests with internet age security in mind. A typical exemplar of this viewpoint writes
[Cheating] is a problem with folks using antiquated methods for tests, contests, etc. – methods that are a poor fit to the current information age. Any problems they encounter should be fixed at the source – not kludged here.
I strongly disagree.