Timeline for Algebraic geometry used "externally" (in problems without obvious algebraic structure).
Current License: CC BY-SA 2.5
14 events
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| Jul 24, 2022 at 11:57 | comment | added | The Amplitwist |
The link to eom.springer.de is broken, but the article can now be found at encyclopediaofmath.org/wiki/Schottky_problem.
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| Jun 25, 2010 at 22:15 | comment | added | Victor Protsak | I am not entirely sure what you are looking for. In the context of the Sato Grassmanian, KP hierarchy is more natural to consider than KdV (no periodicity). You certainly don't need geometric Langlands program in order to analyze either one: see old Segal-Wilson paper (Publ IHES 61) and Pressley-Segal's book. I would say that the connection goes the other way. | |
| Jun 25, 2010 at 4:46 | comment | added | CFZ | Victor, papers on arxiv by Ben-Zvi & Nevins give an analysis of KP hierarchy using Wilson's grassmannian as seen from Geometric Langlands. What I was wondering if the seemingly easier case of KdV was already handled. | |
| Jun 25, 2010 at 0:31 | comment | added | Victor Protsak | See also George Wilson's Invent Math paper on adelic grassmanians. | |
| Jun 24, 2010 at 20:16 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
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| Jun 23, 2010 at 22:35 | comment | added | Andrey Rekalo | @ mathphysicist: Many thanks for the reference! | |
| Jun 23, 2010 at 22:32 | comment | added | mathphysicist | One could peruse Dubrovin lectures on the subject: people.sissa.it/~dubrovin/rsnleq_web.pdf | |
| Jun 23, 2010 at 21:23 | comment | added | CFZ | In papers on geometric Langlands one sometimes sees discussion ind-schemes (inductive limits) especially including infinite Grassmannians. What I was wondering is whether the KdV-related Grassmannian is understood using algebraic geometry constructs per se (sheaves, cohomology, etc) in addition to having a nice flow on a homogeneous space. Since Langlands stuff seems to be half the discussion on this site I was hoping someone will know! | |
| Jun 23, 2010 at 20:50 | comment | added | Andrey Rekalo | @ CFZ: Thank you for the comment. Unfortunately, I'm not a specialist in soliton equations (let alone the algebro-geometric aspects of the theory) and I only learned a bit about the connection when I was an undergraduate. So I'd better let someone with more knowledge comment on this. | |
| Jun 23, 2010 at 20:33 | comment | added | CFZ | Great answer. Is the Sato infinite-dimensional Grassmannian (on which KdV becomes a linear flow) also understood algebro-geometrically these days, or is it mostly the construction of soliton solutions using algebraic curves and moduli spaces (Krichever et al) that provides the connection? | |
| Jun 23, 2010 at 20:23 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
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| Jun 23, 2010 at 20:07 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
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| Jun 23, 2010 at 20:02 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
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| Jun 23, 2010 at 19:49 | history | answered | Andrey Rekalo | CC BY-SA 2.5 |