Timeline for Research directions in complex differential geometry
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2022 at 12:40 | comment | added | R. van Dobben de Bruyn | One possible answer to this is geometric analysis, which is quite an active subject indeed. This can be paraphrased as "partial differential equations on manifolds", and a substantial portion of it is intended to have applications to complex geometry. Hodge theory is a good historical example of this, and a more recent topic (that is definitely still an active area of research) is the study of Kähler–Einstein metrics. | |
| Oct 2, 2022 at 9:56 | comment | added | Ho Man-Ho | @Z.M Thanks, I will take a look. | |
| Oct 2, 2022 at 9:52 | comment | added | Ho Man-Ho | @AndyPutman I agree with you that questions like this may not get a good answer here. And not sure if there should be something like a wiki page so that every research area in math has a brief description (which would need the contributions of many researchers), so that researchers in other fields could have a rough picture. On the other hand, I cannot say I dislike algebraic geometry, I simply haven't learned it during my graduate study, and it seems I am kind of too old to learn it now (even the basic). Anyway, let see if there is anything which leads me to complex geometry. | |
| Oct 2, 2022 at 7:56 | comment | added | Z. M | Mathematically, I want to point out that things that are classically considered analytic could be accessed via "algebraic" methods by recent works in condensed mathematics, cf. this MO post and Clausen–Scholze's lecture notes. | |
| Oct 2, 2022 at 0:59 | comment | added | Andy Putman | I think you should talk to potential advisors rather than random people on the internet. While I have not voted to close, I would not be surprised if this question ended up being closed (and I also think that questions like this never really get good answers here). I also think that it is unwise to insist that you are never going to learn any particular field. You go where the math leads you -- every time I have insisted that I disliked something, I have eventually been forced to learn it (and so far I have always learned that I actually liked it, once I got over my uninformed prejudices). | |
| Oct 1, 2022 at 20:16 | history | asked | Ho Man-Ho | CC BY-SA 4.0 |