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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
comment 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
comment 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
comment 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
comment 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
comment 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
comment 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
comment 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
comment 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
comment What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
Ah, I see. Thanks!
Apr
8
comment 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
comment 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
comment 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?