Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • Comment about Ackermann function. I don’t know what Ackermann originally wrote, but most texts use A_0(m)=m+1, if I understand correctly.

      diff, v18, current

    • The Idea-section at quasi-Hopf algebra had been confused and wrong. I have removed it and written a new one.

    • a list to be !include-ed in relevant entries as pointer to related entries

      v1, current

    • Just some minimum, for completeness, to go in the list of constructions with Sullivan models

      v1, current

    • Added to the entry fuzzy dark matter pointer to Lee 17 which appeared today on the preprint server. This is just a concise 2.5 page survey of all the available literature, but as such is very useful. For instance it points out this Nature-article:

      • Hsi-Yu Schive, Tzihong Chiueh, Tom Broadhurst, Cosmic structure as the quantum interference of a coherent dark wave, Nature Physics 10, 496–499 (2014) (doi:10.1038/nphys2996)

      which presents numerical simulation of the fuzzy dark matter model compared to experimental data.

    • Page created, but author did not leave any comments.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • a stub, just to make links work for the moment

      v1, current

    • Moved the reference to the Lawvere commentary on Isbell to ’References’.

      diff, v16, current

    • Page created, but author did not leave any comments.

      v1, current

    • I’ve started ordinal analysis, mostly because I was beginning to forget a lot of what I once knew, and I had occasion to look into it again.

      I mainly wanted to get the big table in there for future reference, but I tried to say few general remarks as well. I know there’s not much of an npov on ordinal analysis (yet), but it’s certainly of interest concerning strength of type theories for example.

      I may try to fill in more explanations of undefined terms later, but I’m done for today.

    • starting something. Not done yet but need to save

      v1, current

    • I was thinking/hoping now that a general approach to perturbative QFT should exist, where all Feynman amplitudes are regarded not as singular distributions on M nM^n, but as smooth differential forms on the FM-compactification of the configuration space of nn points. Mentioning this hunch to Igor Khavkine, he immediately recalled having heard Marko Berghoff speak about developing just that in his thesis Berghoff 14.

      v1, current

    • a bare minimum, just for completeness

      v1, current

    • Thomas Holder has been working on Aufhebung. I have edited the formatting a little (added hyperlinks and more Definition-environments, added another subsection header and some more cross-references, cross-linked with duality of opposites).

    • bare minimum, for the moment just so as to record the basic references

      v1, current

    • created dual graviton with nothing but a one-sentence Idea and a reference. (I need that to point to it from 3d supergravity, for completeness).

    • I have been further working on the entry higher category theory and physics. There is still a huge gap between the current state of the entry and the situation that I am hoping to eventually reach, but at least now I have a version that I no longer feel ashamed of.

      Here is what i did:

      • Partitioned the entry in two pieces: 1. “Survey”, and 2. “More details”.

        • The survey bit is supposed to give a quick idea of what the set of the scene of fundamental physics is. It starts with a kind of creation story of physics from \infty-topos theory, which – I think – serves to provide a solid route from just the general abstract concept of space and process to the existence and nature of all σ\sigma-model quantum field theories of “\infty-Chern-Simons theory”-type (which includes quite a few) and moreover – by invoking the “holographic principle of higher category theory” – all their boundary theories, which includes all classical phase space physics.

          The Survey-bit continues with indicating the formalization of the result of quantizing all these to full extended quantum field theories. It ends with a section meant to indicate what is and what is not yet known about the quantization step itself. This is currently the largest gap in the mathematical (and necessarily higher categorical) formalization of physics: we have a fairly good idea of the mathematics that describes geometric background structure for physics and a fairly good idea of the axioms satisfied by the quantum theories obtained from these, but the step which takes the former to the latter is not yet well understood.

        • The “More details”-bit is stubby. I mainly added one fairly long subsection on the topic of “Gauge theory”, where I roughly follow the historical route that eventually led to the understanding that gauge fields are modeled by cocycles in higher (nonabelian) differential cohomology.

      • Apart from this I added more references and some cross-links.

      I know that the entry is still very imperfect. If you feel like pointing out all the stuff that is still missing, consider adding at least some keywords directly into the entry.

    • collecting some references, not done yet

      v1, current

    • In the entry spacetime there used to be a subsection on the “hole argument”. It started out with Tim van Beek recalling the “hole paradox” and then continuing with me adding a lengthy discussion, with the result being an organizational mess as far as the poor entry that hosted it was concerned.

      I have now moved that material into its own entry hole paradox, gave it a coherent and concise (I hope) idea-section, and cross-linked with general covariance.

      The section “The hole argument” there is what Tim had originally written, I think, whereas the section Discussion is what I had added back then.

      I am not claiming that that “discussion” of mine is necessarily particular well formulated, but I claim that it gets to the point.

      Looking around I see that one finds the weirdest things being said about the “hole paradox”. For instance the first sentence this article here.

      I am not proposing that we get into this. All I wanted to achieve here is to clean up the poor entry spacetime.

    • I have tried to improve the list of references at stable homotopy theory and related entries a bit. I think the key for having a satisfactory experience with the non-\infty-categorical literature reflecting the state of the art, is to first have a general but quick survey, and then turn for the details of highly structured ring spectra to a comprehensive reference on S-modules or orthogonal spectra. So I have tried to make that better visible in the list of reference.

      I find that for the first point (general but quick survey) Malkiewich 14 is the best that I have seen.

      Of the highly structured models, probably orthogonal spectra maximize efficiency. A slight issue as far as references go is that the maybe best comprehensive account of their theory is Schwede’s Global homotopy theory, which presents something more general than beginners may want to see (on the other hand, beginners often don’t know what they really want). In any case, I have kept adding this book reference as a reference for orthogonal spectra, joint with the comment that the inclined reader is to chooce the collection \mathcal{F} of groups as trivial, throughout.