Timeline for The importance of generating series in Algebraic Geometry
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2013 at 22:49 | comment | added | Urs Schreiber | I think the crucial sentence in that article is this one (p. 917/(6 of 15)): "Within quantum theory it makes perfect sense to combine all the numbers into a single generating function In fact, this function has a straightforward physical interpretation. It can be seen as a probability amplitude for a string" | |
| Sep 23, 2013 at 21:11 | vote | accept | Brenin | ||
| Sep 21, 2013 at 17:26 | comment | added | Brenin | @VesselinDimitrov: the article you indicated to me is amazing. Thank you, I did not know it and it enlightened my morning. | |
| Sep 21, 2013 at 0:44 | comment | added | Vesselin Dimitrov | Plainly, to paraphrase a line from an article (Geometry and physics, Phil. Trans. R. Soc. A 2010, highly recommended) by Atiyah, Dijkgraaf, and Hitchin, dualities in physics, including the one that underlies the enumeration formula you mention, are often [always?] "captured by a generating function that allows two different expansions." This is true of other mathematical formulas as well. In this way generating series are more than just a formal book keeping device for recurrence relations among coefficients. In any case they fully deserve to be called functions rather than power series. | |
| Sep 20, 2013 at 22:41 | answer | added | Colin McLarty | timeline score: 2 | |
| Sep 20, 2013 at 21:56 | comment | added | Qiaochu Yuan | The obvious guess is that the entire series has some meaning, e.g. maybe it is the asymptotic expansion of some path integral or something. | |
| Sep 20, 2013 at 21:36 | answer | added | John Salvatierrez | timeline score: 1 | |
| Sep 20, 2013 at 20:32 | history | asked | Brenin | CC BY-SA 3.0 |