Timeline for Number Theory and Gravity
Current License: CC BY-SA 4.0
16 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jun 2, 2019 at 14:09 | comment | added | David Ben-Zvi | The only significant interaction I'm aware of is the suggestion in arxiv.org/abs/1707.01292 of a factorization structure in GL_n geometric Langlands with respect to n (ie we think of the GL_n as coming from a stack of branes and move their locations around in the transverse direction). This is closely related to the Hall-algebraic interpretation of the Langlands correspondence for function fields (associated with Kapranov). | |
| Feb 18, 2019 at 15:42 | comment | added | AHusain | @WillSawin I was thinking of what happens with $n \to \infty$ without the GL twist. That might not be as helpful as I thought. | |
| Feb 18, 2019 at 15:24 | comment | added | Will Sawin | @AHusain I know of nothing about planar limits, nor do I know of any reference. I could give a short description of the stabilization that is observed on the Langlands side and what it might correspond to in the Kapustin-Witten picture, but I don't know anything about what these limits mean in the physical side. | |
| Feb 17, 2019 at 21:23 | comment | added | AHusain | @WillSawin Is there a reference for that comparing that stabilization on the Langlands side vs simplification by taking planar limit on Kapustin-Witten perspective? | |
| Feb 8, 2019 at 4:39 | comment | added | wonderich | because that may be the way physicists like --- the people who write the papers want to understand the math by a "physics reformulated" story? | |
| Feb 8, 2019 at 3:11 | comment | added | Will Sawin | @wonderich I don't know if anyone really aims for a reformulation. Why do you think that? | |
| Feb 7, 2019 at 16:30 | comment | added | wonderich | @Will Sawin, thanks, Will +1, I changed to "geometric analog (aim for a reformulation)" is this better? | |
| Feb 7, 2019 at 16:30 | history | edited | wonderich | CC BY-SA 4.0 |
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| Feb 6, 2019 at 12:27 | comment | added | Will Sawin | You should say that geometric Langlands is an analogue of the classical Langlands, rather than a reformulation. | |
| Feb 6, 2019 at 12:26 | comment | added | Will Sawin | There are some calculations in the Langlands program for $GL_n$ that have some kind of stabilization in the large $n$ limit. These have analogues in the geometric Langlands program, thus surely analogues in the Kapustin-Witten field theory picture, thus maybe analogues in some string theory / M-theory. But all the calculations I know of are ones where the expected answer is something simple, so it's not clear whether the gravity analogue will help for the number theory at all. The simplest example is that the cohomology of $\operatorname{Bun}_{GL_n}$ stabilizes as $n\to \infty$. | |
| Feb 4, 2019 at 18:57 | history | edited | wonderich | CC BY-SA 4.0 |
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| Feb 4, 2019 at 6:55 | review | Close votes | |||
| Feb 8, 2019 at 20:55 | |||||
| Feb 4, 2019 at 6:32 | comment | added | AHusain | That may be an approach of making an already difficult problem (GL) into an almost impossible one of gravity. Also worse if N of gauge group is too small. | |
| Feb 4, 2019 at 4:38 | history | edited | wonderich | CC BY-SA 4.0 |
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| Feb 4, 2019 at 0:54 | history | asked | wonderich | CC BY-SA 4.0 |