Timeline for Are overlaps among {algebraic geometry, arithmetic geometry, algebraic number theory} growing?
Current License: CC BY-SA 3.0
16 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 16, 2016 at 11:13 | comment | added | tracing | Also: Wei Ho is a woman. (So a comment above should read "from her article" $\dots$ .) | |
| Mar 16, 2016 at 11:12 | comment | added | tracing | Arithmetic geometry, arithmetic algebraic geometry, and Diophantine geometry are not precisely defined. (Of course no area of math is precisely defined, but these even less so, in my view.) But they all roughly refer to the algebro-geometric aspects of modern number theory. It's to some extent a matter of taste whether a person calls themselves an arithmetic geometer or a number theorist. (E.g. I call myself a number theorist, and have served on the NSF's number theory panel, and also on its arithmetic geometry panel. And I believe my proposals have been reviewed by both panels too.) | |
| Dec 13, 2015 at 1:53 | comment | added | Joseph O'Rourke | @PrimeRibeyeDeal: It seems the first two terms do not have fixed meaning, just slightly different emphases. The third, Diophantine geometry, appears to focus on an approach to solving Diophantine equations, with Falting's theorem the prime example. | |
| Dec 12, 2015 at 21:46 | comment | added | PrimeRibeyeDeal | Are there distinctions between arithmetic geometry, arithmetic algebraic geometry, and Diophantine geometry? Also, are there any other terms floating around? | |
| Jul 14, 2013 at 16:55 | comment | added | Joseph O'Rourke | Wei Ho: "A large part of modern arithmetic geometry is dedicated to or motivated by the study of rational points on varieties." From his article, "How many rational points does a random curve have?" | |
| Jul 8, 2013 at 13:50 | comment | added | Martin Brandenburg | In your diagram algebraic topology is missing (motivic homotopy theory), but then also category theory (noncommutative geometry, higher category theory), etc. I've heard several people saying something like "Everything is connected to everything." and agree more and more with that. | |
| Jul 7, 2013 at 14:23 | vote | accept | Joseph O'Rourke | ||
| Jul 6, 2013 at 16:53 | comment | added | Matt | I'm actually somewhat confused about what is meant by "arithmetic geometry" or "algebraic geometry". In my mind arithmetic geometry doesn't merely have some overlap with algebraic geometry but is a proper subset of it because it is the study of schemes and "varieties" over non-algebraically closed fields, positive characteristic fields, or arithmetic bases like $\mathbb{Z}$. Does "algebraic geometry" mean "complex algebraic geometry" to rule these out? | |
| Jul 6, 2013 at 11:44 | comment | added | Joseph O'Rourke | "The arithmetic-geometry tag has no wiki summary, can you help us create it?" :-) | |
| Jul 6, 2013 at 1:32 | comment | added | Joël | What is "arithmetic geometry"? | |
| Jul 5, 2013 at 20:21 | comment | added | Jonathan Beardsley | Don't forget homotopy theorists. We frequently make excursions into all of those fields and steal things. I don't know what that means though. | |
| Jul 5, 2013 at 20:18 | answer | added | Olivier | timeline score: 27 | |
| Jul 5, 2013 at 20:08 | comment | added | Yemon Choi | It seems possible to me that certain fields can have increasing overlap while the number of people able or inclined to work with all these fields stays very small. (This is a small variation on John Stalfos's assessment) | |
| Jul 5, 2013 at 19:24 | comment | added | John Stalfos | I don't think Kline's comment is at odds with this observation, since an individual mathematician at any time works in a tiny corner of a field, even as that field grows larger. I think Atiyah's quote is also compatible by separating the process by which mathematicians research in mathematics(which can and does involve division into specialities) from mathematics itself. I guess I'd interpret Atiyah's statement as saying that the divisions mathematicians make are artificial, rather than somehow inherent to mathematics. | |
| Jul 5, 2013 at 19:16 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |