nklein software

If you read an earlier post of mine about Elsevier’s updated letter to the mathematical community then you may remember that towards the end of the post I claimed that Elsevier was lobbying heavily to have all mention of open access removed from the documents of Horizon 2020, Europe’s “Framework Programme for Research and Innovation”, a claim that was then denied by Alicia Wise, who is Elsevier’s “Director of Universal Access”. Leaving aside who is right about this which may depend rather sensitively on the precise words used to describe what happened, not to mention the interpretation of those words ... [Link]

I noticed the following comment in today’s arXiv update of a paper of Kim and Lusztig: A sign error is corrected; a conjecture is replaced by a theorem. Isn’t that mathematical poetry of a kind? It’s unfortunately a bit too long to be a Haiku… [Link]

The Euler characteristic of topological spaces behaves something like a measure. For example, under suitable hypotheses, χ X∪Y =χ X +χ Y −χ X∩Y . One of the main things you can do with a measure is integrate with respect to it — or ‘against’ it, as they say. So: what happens if you try to integrate against the Euler characteristic? I don’t completely understand the answer myself, but I’ll explain as well as I can. Along the way, we’ll see: how this train of thought helps us to define Euler characteristic how it also leads to the notion of ... [Link]

I don’t fully understand this story, but it is time sensitive. Misha Verbitsky is a complex geometer who is also an active Russian political blogger. Recently, he was arrested by the Russian government while attempting to board a flight out of the country. It turns out he was convicted in absentia of violating the trademark of a man named Igor Pugach, by using an image of Pugach to illustrate a blogpost criticizing Pugach. Verbitsky was fined 300,000 rubles approximately 9,700 dollars and will not be able to leave Russia until he pays the sum. Verbitsky’s blog is here; due to ... [Link]

So there’s this thing invented by Anders Kock called a postulated colimit. It seems like I’ve read his note about them numerous times without really understanding it. I felt like there ought to be some relationship with my theory of exact completions, but I didn’t nail it down precisely in time for the posting of that preprint. Now, however, I think I finally have a grasp on postulated colimits. They do turn out to be nicely related to exact completions, but to find out how, you’ll have to wait for me to update the exact completions paper or figure it ... [Link]

This one was liked well enough on Google+, so I might as well post it here. I have been uploading more photos there, in case anyone is interested. [Link]

This is a continuation of my earlier post on teaching workload. I must say that I got quite tired just from writing that post, reinforcing my feelings that this gig might not last. Academic teaching as it is now is awfully work-intensive, and this workload goes all but unnoticed by those who are benefitting from it. Some of this is of course complaining about the Romans who have not done anything for us lately, but the more important question is whether the service we are providing is really needed on that kind of scale. In 1900, half of American kids ... [Link]

This is a sequel to my previous blog post “Cayley graphs and the geometry of groups“. In that post, the concept of a Cayley graph of a group was used to place some geometry on that group . In this post, we explore a variant of that theme, in which fragments of a Cayley graph on is used to describe the basic algebraic structure of , and in particular on elementary word identities in . Readers who are familiar with either category theory or group homology/cohomology will recognise these concepts lurking not far beneath the surface; we wil remark briefly ... [Link]

Ben Green and I have just uploaded to the arXiv our paper “New bounds for Szemeredi’s theorem, Ia: Progressions of length 4 in finite field geometries revisited“, submitted to Proc. Lond. Math. Soc.. This is both an erratum to, and a replacement for, our previous paper “New bounds for Szemeredi’s theorem. I. Progressions of length 4 in finite field geometries“. The main objective in both papers is to bound the quantity for a vector space over a finite field of characteristic greater than , where is defined as the cardinality of the largest subset of that does not contain an ... [Link]

I’m now going to turn to the Numbers and Sets questions from the same year, 2003. I’ve lost count of the number of times I’ve heard people say that the course is quite easy but the questions on the examples sheets and exams are very hard and “not very closely related to the course”. There is a grain of truth in that: the new concepts you have to grasp in Numbers and Sets are not as difficult as the new concepts you have to grasp in most of the other courses, so in order to give enough substance to Tripos ... [Link]

Update: I decided to close comments on this post and the previous Joy Christian post, because they simply became too depressing for me. I’ve further decided to impose a moratorium, on this blog, on all discussions about the validity of quantum mechanics in the microscopic realm, the reality of quantum entanglement, or the correctness of theorems such as Bell’s Theorem. I might lift the moratorium at some future time. For now, though, life simply feels too short to me, and the actually-interesting questions too numerous. Imagine, for example, that there existed a devoted band of crackpots who believed, for complicated, ... [Link]

Here’s a basic example that comes up if you work with elliptic curves: Let be a prime which is . Let be the elliptic curve over a field of characteristic . Then has an endomorphism . It turns out that, in the group law on , we have . That is to say, plus copies of is trivial. I remember when I learned this trying to check it by hand, and being astonished at how out of reach the computation was. There are nice proofs using higher theory, but shouldn’t you just be able to write down an equation which ... [Link]

Douglas Arnold and Henry Cohn have just posted to the arXiv their article Mathematicians take a stand, which will also appear in the Notices of the AMS shortly. In it they describe the background to the Elsevier boycott, and make a case for more people joining in. It might appear at this point that the boycott is losing steam, but I’m pretty sure this is not the case. A lot has been happening, although too much of it is “behind the scenes”. Elsevier has made some concessions, although these so far seem to mostly miss the point. There’s a rumour ... [Link]

Bill Fulton informs me that there is a user on math.SE whose questions are almost entirely copies of homework questions from Math 592 Algebraic Topology and 597 Real Analysis here at Michigan. In the case of the analysis course, almost every question which had been assigned appeared on math.SE. These courses do not have their problem sets online, so it is extremely unlikely that this is someone self-studying the material at a different location. I am sure this is not the only case. There is an interesting discussion to be had and which has been had before about how the ... [Link]

Although I wouldn’t want to a hit someone while they’re down, hitting a large faceless evil corporation, whose sole purpose is to extract rents from the academic community, while they’re down rather appeals to me. Elsevier just sent out an email announcing amongst many other things, to be blogged about later, I guess they are withdrawing support for the Research Works Act. Elsevier has announced today that we are withdrawing our support for the Research Works Act. In recent weeks, our support for the Act has caused some in the community to question our commitment to serving the global research ... [Link]

A team of six computer scientists Lenstra, Hughes, Augier, Bos, Kleinjung and Wachter are reporting a flaw in the way that certain SSL certificate issuers are generating RSA keys. This is getting significant online coverage at websites like NYTimes, Slashdot and BoingBoing, so I thought I’d try my hand at a low level explanation of the mathematical issues. The goal of RSA is that you can publish a certain large number — called your public key — and anyone can then use that key to generate coded messages that only you can read. You can basically think of the RSA ... [Link]

Let’s suppose, hypothetically, that the Elsevier boycott succeeds in decreasing the importance of many major mathematical journals. Let’s also assume that the basics of the journal system still remain unchanged — academics need to get their work certified by acceptance in journals, acceptance which demonstrates that their work is correct and reaches some particular level of importance. Then we will need a lot of new journals, or new publishers for old journals if more editorial boards jump ship. And those journals will need editors. I would love to hear from people with editorial experience what it would take make editing ... [Link]

The guys at Scholastica some grad students at UChicago just added arXiv integration to their journal management software. It’s pretty impressive, and it seems they’re very actively working on the software. I’m sure they’d be really excited if one upshot of the current debate about publishing was some journals switching to or new journals starting on their software. If journals are going to abandon the big commercial publishers, we need to make sure there are viable alternatives; and part of that is ensuring that the basic software for managing manuscripts and referee reports is up to par. Even if we’re ... [Link]

There’s been lots of great discussion on the future of mathematical publishing in recent weeks, largely inspired by the boycott of Elsevier 1 2 3 . Mostly this has been happening on blogs, particularly Tim Gower’s, but also here and a number of other places. There’s a nice index of this discussion in a wiki page on Michael Nielsen’s site, to the extent that it’s possible to index a discussion happening all over the internet! I think a lot of people find it somewhat frustrating that this discussion is predominantly happening in blog comment threads, however. It’s hard to maintain ... [Link]

I just finished teaching two sections of first semester calculus at the University of Michigan. Michigan calculus is somewhat famous — it is very focused on conceptual and graphical understanding, spends a lot of time on “real world” data, and achieves very high scores in national measures of teaching effectiveness. Moreover, while the course coordinators are highly experienced professionals, almost all of the day-to-day instruction is done by a small army of grad students and postdocs; I was one of the very few tenured or tenure track people teaching calculus this term. I was very curious to see how this ... [Link]

This is the title of a fairly interesting paper, the conclusions of which I would summarise as follows: after the collapse of the Soviet Union there was a sudden drop in the number of papers published by Americans working in fields which had been popular in the Soviet Union, which did not happen in fields which were unpopular there. Their papers were also less cited, and they moved to less prestigious institutions. Collaborating with Soviet immigrants afforded some but not total protection from this effect. Remarkably and not entirely irrelevantly for me; I’m actually a data point in the paper, ... [Link]

The current situation of homotopy type theory reminds me a bit of the dot-com bubble at the turn of the millenium. Back then a technology had appeared which was as powerful as it was new: while everybody had a sure feeling that the technology would have dramatically valuable impact, because it was so new nobody had an actual idea of what that would be. As opposed to other bubbles, that one did not burst because overly optimistic hopes had been unjustifed as such, but because it took a while to understand just how these hopes would be materialized in detail ... [Link]

A few months ago, I got a surprise call from Subra Suresh, director of the National Science Foundation, who told me I was going to share this year’s Alan T. Waterman Award with Robert Wood of Harvard. At first I assumed it was a telemarketing call, since pretty much no one calls my office phone; I use my iPhone exclusively and have trouble even operating my desk phone. Dr. Suresh explained that this was the first time the Waterman would ever be awarded to two people the same year, but that the committee was unanimous in supporting both me and ... [Link]

In a couple of days, we will resume the debate between Aram Harrow and me regarding the possibility of universal quantum computers and quantum fault tolerance. The debate takes place over GLL Godel’s Lost Letter and P=NP blog. The Debate Where were we? My initial post “Perpetual Motion of The 21st Century?” presented my conjectures regarding how noisy quantum computers and noisy quantum evolutions really behave. Aram’s first post was entitled “Flying Machines of the 21st Century?” It mainly dealt with the question “How is it possible that quantum fault-tolerance is impossible or really really hard while classical fault tolerance ... [Link]

I had another long plane flight recently, so I decided to try making another game, to explore exactly what types of mathematical reasoning might be amenable to gamification. I decided to start with one of the simplest types of logical argument and one of the few that avoids the disjunction problem mentioned in the previous post , namely the Aristotelian logic of syllogistic reasoning, most famously exemplified by the classic syllogism: Major premise: All men are mortal. Minor premise: Socrates is a man. Conclusion: Socrates is a mortal. There is a classic collection of logic puzzles of Lewis Carroll from ... [Link]