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The Idea-section at quasi-Hopf algebra had been confused and wrong. I have removed it and written a new one.
Just enough to have the definition and main references, for now. Will create cartesian restriction category soon.
Linked to from partial function.
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:
which presents numerical simulation of the fuzzy dark matter model compared to experimental data.
created Whitehead theorem, including its (oo,1)-topos version
in that context I also created hypercomplete (infinity,1)-topos. maybe that should be merged eventually with hypercompletion.
Added to references:
Brian Munson, Introduction to the manifold calculus of Goodwillie-Weiss (arXiv:1005.1698)
Thomas Willwacher, Configuration spaces of points and real Goodwillie-Weiss calculus, talk at Isaac Newton Institute, 2018.
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.
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 , but as smooth differential forms on the FM-compactification of the configuration space of points. Mentioning this hunch to Igor Khavkine, he immediately recalled having heard Marko Berghoff speak about developing just that in his thesis Berghoff 14.
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).
added rough statement of the general volume conjecture (here), just so that I could point to
which seems to be regarded as a landmark result.
brief category:people-entry for hyperlinking references at 3d-3d correspondence, volume conjecture and elsewhere
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 -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 -model quantum field theories of “-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.
brief category:people-entry for hyperlinking references at 4th generation of fermions
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.
brief category:people-entry for hyperlinking references at stable homotopy theory
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--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 of groups as trivial, throughout.