Timeline for Quantum dynamics on varieties and Salmon Prizes
Current License: CC BY-SA 3.0
32 events
| when toggle format | what | by | license | comment | |
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| Nov 2, 2018 at 16:52 | history | edited | CommunityBot |
replaced http://tea.mathoverflow.net/ with http://mathoverflow.tqft.net/
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Feb 22, 2012 at 18:41 | comment | added | Margaret Friedland | Some progress towards Salmon Conjecture was made and I can attest that at least one of the authors received a portion of Alaskan salmon from Dr. Altman in recognition of the contribution: A proof of the set-theoretic version of the salmon conjecture Shmuel Friedland, Elizabeth Gross arXiv.org > math > arXiv:1104.1776 The question itself and the problems it concerns are well beyond my expertise and interests, but I happen to be married to Shmuel... | |
| Feb 22, 2012 at 12:10 | history | edited | John Sidles | CC BY-SA 3.0 |
fixed link to seminar
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| Feb 22, 2012 at 11:46 | comment | added | John Sidles | As a further update, it turns out that the Salmon Prize is offered for progress in this class of conjecture, and the question-asked now links to this prize. | |
| Feb 22, 2012 at 11:42 | history | edited | John Sidles | CC BY-SA 3.0 |
Shortened title and new references to Elizabeth Allman's "Salmon Prize"; Post Made Community Wiki
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| Feb 14, 2012 at 11:51 | comment | added | John Sidles | As an update, a key reference regarding quantum dynamics on projective varieties turns out to be Hirotachi Abo; Giorgio Ottaviani; Chris Peterson, "Induction for secant varieties of Segre varieties", Transactions of the AMS (2008). Combining the proof technologies of Abo et al. with numerical experiments via our quantum systems engineering software yields a plausible conjecture for a complete classification of "lion" varieties, and this conjectured varietal classification will be the subject of an MOL question in the next couple of weeks. | |
| Feb 14, 2012 at 1:58 | history | edited | John Sidles | CC BY-SA 3.0 |
Added summary intent
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| Feb 14, 2012 at 1:45 | comment | added | John Sidles | @Qiaochu, in agreement with your point, the unique virtue of MOF surely is its exclusive focus upon well-posed math questions. And yet in agreement too with Gil Kalai, many folks (but not all) appreciate physical/practical motivations. And finally (in my own opinion) it is neither necessary, nor feasible, nor even desirable that everyone think & post alike in these matters. So to strike a three-way balance, my next post will be a double-distilled pure-math question, whose physical/practical motivations are described separately, below a bar (where folks can ignore them or not, as preferred). | |
| Feb 14, 2012 at 1:27 | comment | added | Qiaochu Yuan | @John: I do not think that MO questions should be geared towards reconciling cultures. That's what blog posts are for. | |
| Feb 14, 2012 at 0:43 | comment | added | John Sidles | @Gil Kalai and @Marcin Kotowski, you are both entirely correct. The question asked arose when our UW QSE Group noticed certain numerical "miracles" in our quantum spin simulation software. In this regard, please let me commend in Joseph Landsberg's book Tensors: Geometry and Applications his short essay of Section 0.3, titled "Clash of Cultures" (books.google.com/books?id=JTjv3DTvxZIC&pg=PR17). Thus, next week I hope to post a focused question to help reconcile these cultures, in accord with Hestenes' saying: "Geometry without algebra is dumb, algebra without geometry is blind." | |
| Feb 13, 2012 at 22:27 | comment | added | Gil Kalai | What could be very helpful for understanding the question is a simple overview of the background and down to earth description of the conjecture. It looks that John is referring to a method, (perhaps even a method used in practice) to replace a large Hilbert state space of a quantum system by a much lower dimensional algebraic variety of some sort. Taking this variety as a the space of states you can still (but I dont understand how) discuss quantum-like evolutions. John's conjecture is that such much lower dimensional approximation give a good approximation to practical quantum evoltions. | |
| Feb 13, 2012 at 14:57 | comment | added | John Sidles | @Qiaochu your suggestion is sound, and in response the question now is shortened, focused, and now begins with a suggested answer than draws upon Joseph Landsberg's very recent (and dauntingly comprehensive) monograph Tensors: Geometry and Applications (December 2011). It turns out too that certain key results are accessibly surveyed in Landsberg's Bull. AMS article "Geometry and the complexity of matrix multiplication" (2008). These essentially are the references sought, and so I thank you and everyone here on MOF for comments and suggestions that have helped in finding them. | |
| Feb 13, 2012 at 14:36 | history | edited | John Sidles | CC BY-SA 3.0 |
immaterial font correction
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| Feb 13, 2012 at 6:30 | comment | added | Qiaochu Yuan | I agree with Marcin. The question is still much, much too long. | |
| Feb 12, 2012 at 22:59 | history | edited | John Sidles | CC BY-SA 3.0 |
minor adjustments
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| Feb 12, 2012 at 18:42 | comment | added | John Sidles | Please let me say that I consider the various comments on my question to have been (all of them) very valuable, and so later today (Sunday) I will post an amended version that attempts to address these comments all-at-once. Especially I appreciate and am grateful for Theo Johnson-Freyd's comments---as pertaining both narrowly to notation and broadly to mathematical context---and it has been exceedingly enjoyable to watch this question help Theo (albeit inadvertently) earn MOF's first Gold Reversal Medal. So thank you all very much! | |
| Feb 12, 2012 at 5:33 | comment | added | Andy Putman | I started a meta thread here : tea.mathoverflow.net/discussion/1307/… Please vote this up so that it becomes more visible. | |
| Feb 12, 2012 at 0:35 | comment | added | Marcin Kotowski | In short, the question would be much better if OP cut all the hype about STEM, lions, $100,000 rewards, scalable quantum computing etc. and left the underlying mathematical question clear and well defined (in particular, it should be obvious why the question is not trivial). | |
| Feb 12, 2012 at 0:31 | comment | added | Marcin Kotowski | @Andres Calcedo: the question is simply difficult to comprehend - it either reduces to a trivial linear algebraic fact (see Theo's answer) or involves some unspecified "algebraic constraints" which are not at all clear from the question. Plus, a lot of "background" (thermodynamics, quantum varieties, talk about pullbacks) makes it even more muddled, the relation to quantum computing is completely opaque (even for me, who does research in quantum computing), and frankly speaking, sentences with "STEM" being every other word don't seem to hep. | |
| Feb 12, 2012 at 0:14 | comment | added | Andrés E. Caicedo | Would someone please comment on why the aggressive downvoting? | |
| Feb 11, 2012 at 13:51 | history | edited | John Sidles | CC BY-SA 3.0 |
Added an *important* caveat regarding linearity
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| Feb 10, 2012 at 21:31 | answer | added | Theo Johnson-Freyd | timeline score: 35 | |
| Feb 10, 2012 at 21:25 | history | edited | John Sidles | CC BY-SA 3.0 |
Added thermodynamical link
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| Feb 10, 2012 at 20:45 | comment | added | John Sidles | Joseph, I think many folks are coming to appreciate that, when it comes to quantum computing, the boundaries between "possible", "infeasible", and "impossible" are not as mathematically or physically natural as everyone would like. The SHLT question asked here on MOFL was conceived with a view toward illuminating some of the challenges associated to these boundaries. Broadly, the idea is to get (hopefully) more clear on the mathematical foundations here at MOFL, then build upon those math foundations next week in science-and-engineering discussions on Godel's Lost Letter. | |
| Feb 10, 2012 at 20:38 | history | edited | John Sidles | CC BY-SA 3.0 |
Details added to make examples easier to follow.
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| Feb 10, 2012 at 20:36 | comment | added | Joseph O'Rourke | @John: How certain are you that your Hypotheses are equivalent to showing that "scalable quantum computing is impossible in the physical world"? Your phrase "practicable quantum experiment" seems at odds with Scott's "impossible"... | |
| Feb 10, 2012 at 20:13 | comment | added | John Sidles | Gerhard, that is a fine suggestion ... it's done! | |
| Feb 10, 2012 at 20:12 | history | edited | John Sidles | CC BY-SA 3.0 |
title amended per request
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| Feb 10, 2012 at 20:06 | history | edited | John Sidles | CC BY-SA 3.0 |
a minor etymological clarification
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| Feb 10, 2012 at 20:00 | comment | added | Gerhard Paseman | I recommend making the title be less crass and have more class by omitting the dollar amount. Gerhard "Likes Money, Doesn't Love It" Paseman, 2012.02.10 | |
| Feb 10, 2012 at 19:39 | history | asked | John Sidles | CC BY-SA 3.0 |