Timeline for Fundamental motivation for several complex variables [closed]
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 29, 2012 at 22:20 | vote | accept | Steve | ||
| Nov 29, 2012 at 17:24 | history | closed |
fedja Felipe Voloch Chris Godsil David Corwin Suvrit |
not constructive | |
| Nov 28, 2012 at 5:04 | answer | added | Jesse Madnick | timeline score: 7 | |
| Nov 28, 2012 at 1:55 | comment | added | Todd Trimble | I wouldn't mind hearing more about historical motivations for studying several complex variables. I am vaguely aware that the subject is of rather different character than a single complex variable (e.g., domains of holomorphy are more subtle in SCV), but I don't know what were the big problems that drove the subject before it reached maturity. | |
| Nov 27, 2012 at 18:46 | answer | added | anon | timeline score: 4 | |
| Nov 27, 2012 at 17:35 | answer | added | Qfwfq | timeline score: 9 | |
| Nov 27, 2012 at 13:07 | comment | added | Tom Goodwillie | As far as I'm concerned, one-variable complex analysis doesn't need any "general abstract reasons" to justify caring about it. No matter which direction you come at it from, it's beautiful and somehow inevitable. Based on that alone, I trust that SCV is also beautiful and inevitable. I've never got around to studying SCV, but I wish I had. | |
| Nov 27, 2012 at 12:56 | answer | added | Daniel Moskovich | timeline score: 12 | |
| Nov 27, 2012 at 10:18 | answer | added | Igor Khavkine | timeline score: 6 | |
| Nov 27, 2012 at 7:37 | comment | added | anon | The theory of several complex variables is such a rich and beautiful subject I have trouble understanding how anyone can ask the question. For example, the the theory of symmetric Hermitian spaces is quite interesting. | |
| Nov 27, 2012 at 6:54 | answer | added | Francois Ziegler | timeline score: 11 | |
| Nov 27, 2012 at 5:37 | comment | added | fedja | @Steve There are many ways to ask such questions and you chose the one to which my instinctive reaction was "And what motivation do I have to motivate you?". You see, "useful" is a dangerous word ("interesting" and "important" are other two). What interests me should not necessarily interest you and vice versa. There is no common "why". As to "where" I once used the Hormander L^2 bounds to reprove the Bourgain-Milman estimate for the volume product of a symmetric convex body, so I would say "Don't classify, grab whatever you can and try to get away with it". OK, I'll think of a better answer. | |
| Nov 27, 2012 at 5:25 | comment | added | YangMills | "I have not yet seen a real application of SCV in complex algebraic geometry": you can look for example at almost any paper by J-P Demailly | |
| Nov 27, 2012 at 4:42 | answer | added | Alexandre Eremenko | timeline score: 15 | |
| Nov 27, 2012 at 4:41 | comment | added | Steve | @fedja - I, and I suspect a lot of other mathematicians, like to have a general feeling for where and why the different fields of mathematics are useful. I may not have much use for cohomology in my day to day mathematical life, but I know that if I am confronted with a local to global problem, searching for a cohomological interpretation will be useful. Or if my problem is invariant under the action of some group, the representation theory of that group will probably be useful. I know SCV is an important field, I just don't know why yet. Maybe someone here can provide some insight. | |
| Nov 27, 2012 at 4:36 | comment | added | Qiaochu Yuan | It was a suggestion; I don't actually know. Another suggestion: Banach algebras? | |
| Nov 27, 2012 at 4:35 | comment | added | fedja | If you have no motivation for doing something, just don't do it. Neither you, nor the subject will lose much. Voting to close as not a real question. | |
| Nov 27, 2012 at 4:21 | comment | added | Steve | I have not yet seen a real application of SCV in complex algebraic geometry - mostly it is just using the "multivariable calculus" of complex numbers. I don't see where the unique features of SCV come into the picture (namely: domains of holomorphy) | |
| Nov 27, 2012 at 4:15 | comment | added | Qiaochu Yuan | Complex algebraic geometry? | |
| Nov 27, 2012 at 4:12 | history | asked | Steve | CC BY-SA 3.0 |