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brief note on continuous field of C*-algebras
I gave chromatic homotopy theory an Idea-section.
To be expanded eventually…
Stub entry, for the moment just to have a ace for recording this result:
Nico Brown, Carson Cheng, Tanner Jacobi, Maia Karpovich, Matthias Merzenich, David Raucci, Mitchell Riley, Conway’s Game of Life is Omniperiodic [arXiv:2312.02799]
The Physics arXiv Blog, Mathematicians Prove the “Omniperiodicity” of Conway’s Game of Life (Dec 2024)
creating a bare minimum, for the moment only to give a home to these references:
Nik Weaver, Quantum relations [arXiv:1005.0354]
Nik Weaver, Greg Kuperberg, A von Neumann Algebra Approach to Quantum Metrics/Quantum Relations, Memoirs of the AMS 215 (2011) [ams:memo-215-1010]
for when the editing functionality is back, this here is a good textbook to record at quantization:
a stub entry, to make the link work which had long been requested at George Bergman
Under definition 1 of salamander lemma, I fixed a mistake in the definition of where there was a direct sum of two submodules, where there needed to be a sum (i.e., join) instead.
am starting to work on derived smooth manifold, so far just a little bit on the motivation (correction of limits of manifolds)
I am a bit hesitant to add a lot of details from David Spivak’s article, since it seems evident that there is some room to streamline the constructions. I need to think about how to deal with this. One really wants to just specify the site as a geometry (for structured (infinity,1)-toposes) and then just say that a derived manifold is a derived scheme in the sense descrived at generalized scheme on this.
In section 10.1 David Spivak discusses one reason that prevented him from setting things up this way: actually I think this points to the following general issue with the definition of geometry (for structured (infinity,1)-toposes): instead of a Grothendieck topology generated by admissible morphisms the definition ought to just refer to a coverage by admissible morphisms, and instead of the stability under pullback one ought to just consider the coverage-style stability condition.
More later.
recently there were some questions about it here on the nForum: now there is an entry on the Kaluza-Klein mechanism
started some minimum at exceptional field theory (the formulation of 11d supergravity that makes the exceptional U-duality symmetry manifest)
I ended up collecting some references at string phenomenology and accompanying them with a bit of text
Created:
[…]
Urs Schreiber, On nonabelian differential cohomology, March 17, 2008, Slides.
Domenico Fiorenza, Urs Schreiber, Jim Stasheff, Čech cocycles for differential characteristic classes, Advances in Theoretical and Mathematical Physics 16:1 (2012), 149–250, arXiv:1011.4735, doi:10.1007/BF02104916.
Linked to from https://ncatlab.org/nlab/show/orthogonal+factorization+system and https://ncatlab.org/nlab/show/final+functor
Todo: add more proofs of this result.
For some reason the xymatrixes were causing errors so I had to comment them out to submit. Here is an example error:
An error occurred when running pdflatex on the following diagram. \xymatrix@=5em{e \ar[r]^\gamma \ar[dr]_{\gamma’} & GFc \ar[d]^{Gf} \ & GFc’} The error was: Timed out
How can I fix this?
Added a section with a collection of references on intersection laws for black D-branes ending on black NS5-branes. Then I spelled out the case of D6-branes in some detail, collecting the relevant diagrams from the reference EGKRS00, and used this to identify the corresponding M-theory lift by the M5-brane near horizon ADE-orbifolds of the 4-sphere.
Added an example (dR cohomology for spheres) with a very sketchy proof sketch. More examples, worked out in more detail, to follow. Might make a de Rham cohomology page and move the examples there.
Mark Moon
added to Grothendieck construction a section Adjoints to the Grothendieck construction
There I talk about the left adjoint to the Grothendieck construction the way it is traditionally written in the literature, and then make a remark on how one can look at this from a slightly different perspective, which then is the perspective that seamlessly leads over to Lurie's realization of the (oo,1)-Grothendieck construction.
There is a CLAIM there which is maybe not entirely obvious, but straightforward to check. I'll provide the proof later.
starting a collection of references on Seiberg-Witten curves, to be !include-ed into relevant entries (such as to help sync the references at Seiberg-Witten theory and D=4 N=2 SYM, which have a large overlap)
I gave Seiberg-Witten theory an Idea-paragraph, added the orinal reference and cross-linked with N=2 D=4 super Yang-Mills theory and with electric-magnetic duality.
moving this old query box out of the entry
+– {.query} Tim Is the first statement above correct? -groups are examples of strict (n+1)-fold categories, not strict n=categories or am I missing something? (28-09-2010<- corrected)
Ronnie Agreed, and I have corrected that. This is important since an n-category internal to Grp is equivalent to a single vertex crossed complex of length .
It is not so clear how to construct a homotopical functor from -cubes of non pointed spaces, and what should be the receiving category. =–
Stub for topological string with redirect topological string theory.
stub for cooperad
created a stub for holographic entanglement entropy in reaction to this MO question.