Timeline for Strict applications of deformation theory in which to dip one's toe
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23, 2013 at 20:30 | comment | added | roy smith | Smale's famous result that one can turn a sphere smoothly inside out without wrinkling it was proved by computing deformations. | |
| Jun 21, 2013 at 17:20 | comment | added | Ariyan Javanpeykar | The following paper by Richard Pink (and the references in this paper) use deformation theory to give some beautiful applications to quadratic morphisms: arxiv.org/abs/1305.2841 | |
| Jun 21, 2013 at 10:44 | answer | added | Misha | timeline score: 7 | |
| Jun 20, 2013 at 17:56 | comment | added | Jonathan Beardsley | I mean, I guess it's more of a "program" than a problem. The idea being that if we let $\hbar$ go to zero we get the "classical limit." But if we take some "infinitesimal neighborhood" of letting $\hbar$ go to zero (i.e. a deformation) we get some that sort of is like quantum mechanics, or something. I don't really know any physics, lol. | |
| Jun 20, 2013 at 16:08 | comment | added | Dylan Wilson | @Jon: I know absolutely zero things about that, so in particular I dunno if it fits my criteria either :) | |
| Jun 20, 2013 at 15:12 | comment | added | Jonathan Beardsley | Deformation quantization in physics is a pretty amazing picture. Dunno if that fits your criteria. | |
| Jun 20, 2013 at 14:59 | comment | added | Dylan Wilson | @Dan: Sorry, I was missing a hypothesis and now the argument goes "M_g is quasi-compact and H^1 of the automorphism group of a curve over a finite field is finite." @Jason: Hence my hesitation... I've added that tag, apologies for the inconvenience. | |
| Jun 20, 2013 at 14:57 | history | edited | Dylan Wilson | CC BY-SA 3.0 |
missing hypothesis, added tag
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| Jun 20, 2013 at 11:52 | comment | added | Jason Starr | I kind of despise these types of questions. Isn't there some kind of tag, like "soft question", to flag this kind of question. | |
| Jun 20, 2013 at 11:09 | comment | added | Dan Petersen | What do you mean by point (3)? | |
| Jun 20, 2013 at 7:20 | answer | added | Francesco Polizzi | timeline score: 26 | |
| Jun 20, 2013 at 6:34 | comment | added | Dylan Wilson | Silly of me to forget to mention Goerss-Hopkins obstruction theory!! And of course I'm omitting the whole derived story- that's what I really want to get at, but I was hoping to get some of the more classical or algebraic story for the purposes of this question. In any event some of the other references I hadn't heard of- looks like lots of fun! Thanks Sean :) | |
| Jun 20, 2013 at 6:23 | comment | added | Sean Tilson | The work of Robinson and Angeltveit on the multiplication of Morava $K$-theory is done via a form of obstruction theory. Also, the Goerss-Hopkins-Miller theorem is done this way as well. I believe Lurie's proof is along these lines too. Or at least, that is how I would phrase the results. Baker-Richter have papers on Gamma-cohomology which is intimately related, as is the work of Basterra-Mandell on TAQ. I recommend a perusal of Mathscinet as you may stumble on other gems while you are digging (I always do whenever I look at any of the papers by any of those authors). | |
| Jun 20, 2013 at 4:18 | history | asked | Dylan Wilson | CC BY-SA 3.0 |