Timeline for Poincaré Conjecture and the Shape of the Universe
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 15, 2017 at 0:56 | history | edited | Richard Stanley | CC BY-SA 3.0 |
corrected spelling of "maybe"
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| Dec 26, 2009 at 2:50 | comment | added | Greg Kuperberg | That is a very flattering compliment! I am not sure how much I deserve it, but thank you. Certainly in the case of condensed matter physics, my answer is not so creative. I have been working in quantum computation, and in that area everyone knows about the connection between anyons and quantum link invariants. See for instance arxiv.org/abs/0704.2241 . Benjamin Mann at DARPA might well have heard about this work, or possibly not. | |
| Dec 26, 2009 at 1:02 | vote | accept | Shake Baby | ||
| Dec 25, 2009 at 23:53 | comment | added | Pete L. Clark | @Greg -- Now you remind me of my AP English teacher, Dr. Phillips. He was also brilliant, widely learned (once in class he digressed to talk about Russell and Whitehead's Principia Mathematica) and so creative that, if you didn't have anything better to say, it was sometimes a reasonable strategy to write an essay suggesting connections between things when you yourself could not see them: he could, and would, often fill in the details to make your thesis look reasonable and sound. But of course it doesn't mean that you knew what you were talking about, only that he really did. | |
| Dec 25, 2009 at 8:32 | comment | added | Greg Kuperberg | Also, Pete, the question you quoted could be a reference to something legitimate: Quantum link invariants at a root of unity such as the Jones polynomial seem to be a valid model for the quantum state of certain 2-dimensional condensed matter systems. Still, the question as stated is a grandiose variation that does not even mention quantum invariants. | |
| Dec 25, 2009 at 8:24 | comment | added | Greg Kuperberg | I don't want to knock DARPA too much for trying to do good, but I have to agree that their list is a strange imitation of Hilbert's list of 23 problems. For one thing, the list asks for the cosmological implications of the smooth Poincare conjecture in four dimensions, not the Poincare conjecture solved by Perelman. math.utk.edu/~vasili/refs/darpa07.MathChallenges.html | |
| Dec 25, 2009 at 7:49 | comment | added | Pete L. Clark | Just to be clear, it is not the original question that I find risible but rather DARPA's challenge. It reminds me of an episode of NUMBERS where the premise was that a mathematician who had claimed to solve the Riemann Hypothesis was being extorted by criminals who wanted to exploit fast factorization algorithms. What can you do as an engineer with the Geometrization Theorem that you couldn't do with the Geometrization Conjecture? | |
| Dec 25, 2009 at 2:58 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
Extended answer
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| Dec 25, 2009 at 0:58 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
added 109 characters in body
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| Dec 24, 2009 at 23:56 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |