nklein software

For better or worse, I’m now offering a US$100,000 award for a demonstration, convincing to me, that scalable quantum computing is impossible in the physical world. This award has no time limit other than my death, and is entirely at my discretion though if you want to convince me, a good approach would be to convince most of the physics community first . I might, also at my discretion, decide to split the award among several people or groups, or give a smaller award for a discovery that dramatically weakens the possibility of scalable QC while still leaving it open. ... [Link]

As many people have pointed out, to get to a new and better system for dealing with mathematical papers, a positive strategy of actually setting up a new system might work rather better than complaining about the current system. Or rather, since it seems unlikely that one can simply invent ex nihilo a system that’s satisfactory in all respects, one should set up systems in the plural and see which ones work and catch on. I’ve already had a go at suggesting a system, back in this post and this post. Another system that has been advocated, which I also ... [Link]

Van Vu and I have just uploaded to the arXiv our paper “Random matrices: The Universality phenomenon for Wigner ensembles“. This survey is a longer version 58 pages of a previous short survey we wrote up a few months ago. The survey focuses on recent progress in understanding the universality phenomenon for Hermitian Wigner ensembles, of which the Gaussian Unitary Ensemble GUE is the most well known. The one-sentence summary of this progress is that many of the asymptotic spectral statistics e.g. correlation functions, eigenvalue gaps, determinants, etc. that were previously known for GUE matrices, are now known for very ... [Link]

Heavier than air flight of the 21 century? The very first post on this blog entitled “Combinatorics, Mathematics, Academics, Polemics, …” asked the question “Are mathematical debates possible?” We also had posts devoted to debates and to controversies. A few days ago, the first post in a discussion between Aram Harrow, a brilliant computer scientists and quantum information researcher and a decorated debator , and myself on quantum error correction was launched in Dick Lipton and Ken Regan’s big-league blog, Gödel’s Lost Letter and P=NP. The central question we would like to discuss is: Are universal quantum computers based on ... [Link]

I’ve just uploaded to the arXiv my paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. The main result of the paper is as stated in the title, and is in the spirit of though significantly weaker than the even Goldbach conjecture every even natural number is the sum of at most two primes and odd Goldbach conjecture every odd natural number greater than 1 is the sum of at most three primes . It also improves on a result of Ramaré that every even natural number is the ... [Link]

It can be very rewarding to read old mathematical papers, in terms of accessing insights and ideas that may have been filtered out in later transformations of the results they contain. In my modest experience, this does not extend to notation and terminology, and it is much easier to appreciate the insights in question after translating them into modern language and formalism. This is an area where, maybe, progress is usually fairly steady. But still, there can be exceptions. I was recently rather struck, while reading the recently published collection of letters between Henri Cartan and André Weil, to discover ... [Link]

These two links have homeomorphic exteriors. They’re both strongly invertible. Let’s quotient the first link by its strong inversion to get a tangle. Then we’ll isotop that tangle around and eventually take its double branched cover to get the second. Notice that this homeomorphism swaps the red and blue meridians and longitudes. [Link]

A few days ago, inspired by this recent post of Tim Gowers, a web page entitled “the cost of knowledge” has been set up as a location for mathematicians and other academics to declare a protest against the academic publishing practices of Reed Elsevier, in particular with regard to their exceptionally high journal prices, their policy of “bundling” journals together so that libraries are forced to purchase subscriptions to large numbers of low-quality journals in order to gain access to a handful of high-quality journals, and their opposition to the open access movement as manifested, for instance, in their lobbying ... [Link]

I’m still considering whether to sign on to the Elsevier boycott. But, in preparation, I’ve started thinking about which Elsevier journals would be hard to find replacements for. This is tricky for me because I really don’t know much about different journals. My algorithm for choosing a place to submit is 1 see if one of my co-authors has an opinion 2 ask someone more senior 3 look at the papers I cite and see who published them. I thought I’d start a comment thread for people to recommend journals, or to describe niches which they don’t know of a ... [Link]

I keep feeling I should comment on the kerfuffle around Tim Gowers and Elsevier. I had some similar thoughts way back when, though I found that I actually did not have the necessary chutzpah to respond to referee requests as I suggested therein. At the moment, I really find myself just wishing I understood the situation better. On Gower’s blog, we’ve had the response from within Elsevier; I don’t find it particularly convincing, but what do you expect. I don’t think that anyone disagrees that at one point commercial publishers provided a service learned societies didn’t have the resources to ... [Link]

I was messing around this morning and I discovered the following, which seemed cute enough to share. In this post, I’ll make what strikes me as a very reasonable attempt to define for not an integer. Will I get the function? Wait and see! We have . So, by basic complex analysis, , where the integral is taken along a loop around the origin. This formula is also morally right for a negative integer: wants to be $\infty$ when because , so should be infinity, and likewise for the other negative integers . So wants to be zero for and, ... [Link]

It probably sounds disingenuous of me to say this, but when I sat down to write a post about Elsevier I wasn’t really trying to start a campaign. My intention was merely to make public, and a little more rigid, a policy that I and many others had already been applying, in my case without much difficulty, for several years. The idea of setting up a website occurred to me as I was writing the post: I considered it and still consider it not as a petition to Elsevier to change its ways — since I don’t believe there is ... [Link]

Van Vu and I have just uploaded to the arXiv our paper Random matrices: Sharp concentration of eigenvalues, submitted to the Electronic Journal of Probability. As with many of our previous papers, this paper is concerned with the distribution of the eigenvalues of a random Wigner matrix such as a matrix drawn from the Gaussian Unitary Ensemble GUE or Gaussian Orthogonal Ensemble GOE . To simplify the discussion we shall mostly restrict attention to the bulk of the spectrum, i.e. to eigenvalues with for some fixed 0}' title='{\delta>0}' class='latex' />, although analogues of most of the results below have also ... [Link]

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One of the most fundamental principles in Fourier analysis is the uncertainty principle. It does not have a single canonical formulation, but one typical informal description of the principle is that if a function is restricted to a narrow region of physical space, then its Fourier transform must be necessarily “smeared out” over a broad region of frequency space. Some versions of the uncertainty principle are discussed in this previous blog post. In this post I would like to highlight a useful instance of the uncertainty principle, due to Hugh Montgomery, which is useful in analytic number theory contexts. Specifically, ... [Link]

In 1964, Kemperman established the following result: Theorem 1 Let be a compact connected group, with a Haar probability measure . Let be compact subsets of . Then Remark 1 The estimate is sharp, as can be seen by considering the case when is a unit circle, and are arcs; similarly if is any compact connected group that projects onto the circle. The connectedness hypothesis is essential, as can be seen by considering what happens if and are a non-trivial open subgroup of . For locally compact connected groups which are unimodular but not compact, there is an analogous statement, ... [Link]

Emmanuel Breuillard, Ben Green and I have just uploaded to the arXiv the short paper “A nilpotent Freiman dimension lemma“, submitted to the special volume of the European Journal of Combinatorics in honour of Yahya Ould Hamidoune. This paper is a nonabelian or more precisely, nilpotent variant of the following additive combinatorics lemma of Freiman: Freiman’s lemma. Let A be a finite subset of a Euclidean space with . Then A is contained in an affine subspace of dimension at most . This can be viewed as a “cheap” version of the more well known theorem of Freiman that places ... [Link]

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Van Vu and I have just uploaded to the arXiv our short survey article, “Random matrices: The Four Moment Theorem for Wigner ensembles“, submitted to the MSRI book series, as part of the proceedings on the MSRI semester program on random matrix theory from last year. This is a highly condensed version at 17 pages of a much longer survey currently at about 48 pages, though not completely finished that we are currently working on, devoted to the recent advances in understanding the universality phenomenon for spectral statistics of Wigner matrices. In this abridged version of the survey, we focus ... [Link]

We’ll have some pursuit puzzles over the next couple of weeks; this segment’s puzzle has a simple and elegant solution, but it might take a while to work it out! In the meanwhile, here’s a little discussion about the glass of water problem. Each time we add or subtract 50%, we are multiplying the quantity of water by 1/2 or 3/2. If we began with 1 glass’ worth, at each stage, we’ll have a quantity of the form 3m/2n with m,n>0 Of course that can never equal 1, but we can get very close if m/n is very close to ... [Link]

A few days ago, inspired by this recent post of Tim Gowers, a web page entitled “the cost of knowledge” has been set up as a location for mathematicians and other academics to declare a protest against the academic publishing practices of Reed Elsevier, in particular with regard to their exceptionally high journal prices, their policy of “bundling” journals together so that libraries are forced to purchase subscriptions to large numbers of low-quality journals in order to gain access to a handful of high-quality journals, and their opposition to the open access movement as manifested, for instance, in their lobbying ... [Link]

If you’re in academia and haven’t done so yet, please take a moment to sign this online petition organized by Tyler Neylon, and pledge that you won’t publish, referee, or do editorial work for any Elsevier journals. I’ve been boycotting Elsevier and most other commercial journal publishers—Elsevier is merely the worst since 2004, when I first learned about their rapacious pricing policies. I couldn’t possibly be happier with my choice: unlike most idealistic principles, this one gets you out of onerous work rather than committing you to it! Sure, Elsevier is huge and we’re tiny, but the fight against them ... [Link]

Please take the pledge not to do business with Elsevier. 402 scientists have done it so far: The cost of knowledge. You can separately say you 1 won’t publish with them, 2 won’t referee for them, and/or 3 won’t do editorial work. At least do number 2 : activism is rarely so little work, but when a huge corporation relies so heavily on nasty monopolistic practices and unpaid volunteer labor, they leave themselves open to this. This pledge website got started thanks to Tim Gowers: Tim Gowers, Elsevier: my part in its downfall and http://thecostofknowledge.com. For more, see: Journal publishing ... [Link]