Timeline for Mathematical applications of quantum field theory
Current License: CC BY-SA 4.0
20 events
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| Apr 3, 2020 at 7:33 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added Internet Archive link (the original link is dead.)
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| Nov 26, 2016 at 12:36 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Nov 26, 2016 at 2:09 | history | edited | Bilateral | CC BY-SA 3.0 |
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| Nov 26, 2016 at 1:58 | history | edited | Bilateral | CC BY-SA 3.0 |
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| Nov 26, 2016 at 1:48 | comment | added | Todd Trimble | You did indeed, and thanks again for all your efforts. :-) | |
| Nov 26, 2016 at 1:46 | comment | added | Bilateral | @ToddTrimble I agree with you, and I offered Sarah a couple of examples of solutions to hard problems coming from physics and explained by M. Atiyah (who is going to do it much better than myself). Indeed, thanks to mirror symmetry an outstanding problem in algebraic geometry was solved by physicists. I will edit my answer to explain this fact. | |
| Nov 26, 2016 at 0:22 | comment | added | Todd Trimble | Bilateral: yes, that is true of the original motivations in e.g. symplectic geometry -- how it historically arose -- but on my reading it seems Sarah is asking about feedback into pure mathematics. I am told for example that there are enumeration problems in algebraic geometry whose solutions were inspired by mirror symmetry (as I think you were saying, although I didn't click your link), where it is alleged they'd be hard to find otherwise; that's the kind of thing she's looking for, not historical motivations. Thanks by the way for your edit. | |
| Nov 26, 2016 at 0:13 | comment | added | Bilateral | @ToddTrimble: I can rewrite the answer no problem :). I wrote it in those terms because I find a little bit surprising the tone in which Sarah wrote her question. At least from the point of view of a geometer, it is very hard to completely disregard physics, since the main motivation of many of the problems of interest in geometry comes from physics. For example: why mathematicians started studying symplectic manifolds, which are now one of the most important objects in differential geometry/topology? | |
| Nov 26, 2016 at 0:08 | history | edited | Bilateral | CC BY-SA 3.0 |
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| Nov 25, 2016 at 23:36 | comment | added | Todd Trimble | Sarah, I wouldn't read this answer as implying you are close-minded (maybe the "open-minded" should be edited out to remove this impression). I think both your question and this answer are good ones. For my part, the answer is a kind of stinging reminder that I would be a richer mathematician if I had more physical insight -- I am at least open to that :-). | |
| Nov 25, 2016 at 23:24 | comment | added | Bilateral | @Sarah: What about mirror symmetry, is that important enough for you? Here you have the original article: staff.science.uu.nl/~beuke106/HypergeometricFunctions/COGP.pdf | |
| Nov 25, 2016 at 23:22 | history | edited | Bilateral | CC BY-SA 3.0 |
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| Nov 25, 2016 at 23:19 | comment | added | Bilateral | @Sarah: I was not appealing to any authority. I was mentioning Atiyah's article because it is a beautiful and concise exposition of QFT applications to mathematics by one of the most influential mathematicians of the twentieth century. | |
| Nov 25, 2016 at 23:10 | comment | added | AHusain | @Sarah What are you talking about descendents of the Jones polynomial being useless for? What sort of invariants do you want? | |
| Nov 25, 2016 at 20:31 | comment | added | Sarah | I read it many years ago. I stand by everything I wrote. Appeals to authority are meaningless. | |
| Nov 25, 2016 at 20:31 | comment | added | Bilateral | @Sarah: Read Atiyah's article that I cite. | |
| Nov 25, 2016 at 20:29 | comment | added | Sarah | The rest of your answer is just rhetoric about how I am closed-minded. I won't bother to respond to it, but it certainly convinces me of nothing. | |
| Nov 25, 2016 at 20:29 | comment | added | Sarah | I mentioned gauge theory in my question as something I am bracketing off. I certainly am impressed by the Seiberg-Witten invariants (but I'm not sure that they are really the kinds of things that mathematicians mean these days when they talk about QFT's). The TQFT invariants of knots and 3-manifolds you mention are basically useless for mainstream 3-manifold topology (notice that I am definitely not talking here about invariants of knots that come in some way out of gauge theory, eg Heegaard Floer invariants, but rather about descendents of the Jones polynomial). | |
| Nov 25, 2016 at 20:28 | history | edited | Bilateral | CC BY-SA 3.0 |
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| Nov 25, 2016 at 20:08 | history | answered | Bilateral | CC BY-SA 3.0 |