bio | website | ncatlab.org/nlab/show/… |
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visits | member for | 4 years, 6 months |
seen | 2 days ago | |
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I am a postdoc in maths with a degree in theoretical physics. I am interested in mathematical structures in quantum field theory and string theory, see here.
Apr 12 |
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Are $G$-spectra the same as modules over a “group ring spectrum”?
There is now at least a useful pointer on the nLab page on Mackey functors. Maybe somebody has the energy to add more. |
Apr 11 |
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What is to tmf as KR is to KO?
I see now that essentialy what I just suggested had already been conjectured on p. 3 in Igor Kriz, Hisham Sati, "Type II string theory and modularity" arxiv.org/abs/hep-th/0501060 |
Apr 11 |
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What is to tmf as KR is to KO?
...is the twist of an equivariant version of $tmf$. By this story, I shouldn't be fighting the fact that the literature discusses realizations of $tmf$ as $SL_2(\mathbb{Z}/n\mathbb{Z})$-homotopy fixed points, but should maybe rather be embracing it. (Sorry for the lengthy comment, hope you see what I mean; a decent discussion of this would have to break out of this puny comment functionality here.) |
Apr 11 |
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What is to tmf as KR is to KO?
... and that theory is famously controled by a $\mathrm{SL}_2(\mathbb{Z})$-bundle (being the monodromy bundle of an elliptic fibration). An old argument due to Ashoke Sen (ncatlab.org/nlab/show/F-theory#RelationToOrientifolds) says that the inversion involution inside $SL_2(\mathbb{Z})$ induces the orientifolding, hence that this $SL_2(\mathbb{Z})$-local system is indeed the F-theoretic analog of the $\mathbb{Z}_2$-twist on $\mathrm{KU}$. But now by Mahowald-Rezk and then your work, we have that $SL_2(\mathbb{Z})$ or at least the quotient $SL_2(\hat {\mathbb{Z}})$ is the twist of... |
Apr 11 |
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What is to tmf as KR is to KO?
Thanks again. Here is another thought, but I need two sentences to prepare: So my above question was motivated from string theory considerations: there it is known that the general type II string orientifold background is controled by KR-theory receiving its twists from the "orientifolding" $\mathbb{Z}/2\mathbb{Z}$-bundle on spacetime; and general lore suggests that this scenario has a "lift to M-theory" where K-theory is replaced by elliptic cohomology. Hence my question. But now the type II "lifts to M-theory" are known as "F-theory" (ncatlab.org/nlab/show/F-theory) and that theory... |
Apr 11 |
awarded | Civic Duty |
Apr 10 |
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What is to tmf as KR is to KO?
Thanks for the comments! I am reading Hill-Lawson now with some effect. Maybe I should first consider my question with tmf replaced by just Tate K-theory, to warm up. You mention the open question of generalizing the Witten genus: what would even be a plausible replacement of the domain $MO\langle 8\rangle$ as we pass to some cover of $\mathcal{M}_{\overline{ell}}$ for the codomain? |
Apr 9 |
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What is to tmf as KR is to KO?
Or putting on the string theorist hat: what orientifold string physics (where KR-theory appears as the home of the D-brane charges) suggests is that the involution on the worldsheet elliptic curves should be what in physics is called the "worldsheet parity operator" -- which reverses worldsheet orientation... |
Apr 9 |
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What is to tmf as KR is to KO?
I am hoping to see the cover given by the inversion involution on elliptic curves. Is there a subtlety about this obvious idea that I am missing? The 8-fold cover which gives $tmf_1(3)$ quotients to a double cover, I need to understand what that is explicitly. |
Apr 9 |
awarded | Nice Question |
Apr 8 |
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What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
Ah, I see. Thanks! |
Apr 8 |
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p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
But what seems to be missing in the p-adic string literature is the idea of looking systematically at the algebraic geometry of algebraic curves over the p-adic integers. Or at least I don't see this being discussed, this is part of the reason for the above question. |
Apr 8 |
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p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
You find discussion of problems with closed p-adic strings for instance in section 5 of Cottrell's "p-Adic strings and tachyon condensations" ( jfi.uchicago.edu/~tten/teaching/Phys.291/… ) and with more technical details in section 4 of Chekhov et al 89 ( projecteuclid.org/euclid.cmp/1104179635 ) . As one sees there, in this context people try to generalize the ordinary formulas for amplitudes by looking for analogs over the p-adic numbers (for the boundary) and then of quadratic extensions of this in the bulk. This last step remains unclear & inconclusive |
Apr 8 |
revised |
p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
fixed a trivial typo |
Apr 8 |
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What is to tmf as KR is to KO?
Drew and Martin, thanks, so indeed TMF_0(3) is the Z/2Z homotopy fixed points of TMF_1(3); but what about TMF itself? And the compatibility with the action on KU? (Maybe I am missing somehting obvious here...) I was guessing that for TMF itself the construction by Lawson-Naumann is going in the right direction. It bothered me that it only worked 2-locally, but maybe that shouldn't bother me too much. Hm... |
Apr 8 |
awarded | Custodian |
Apr 8 |
revised |
p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)
added one more hyperlink |
Apr 8 |
asked | p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf) |
Apr 7 |
awarded | Nice Question |
Apr 5 |
asked | What is to tmf as KR is to KO? |