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I am at the Croatian black hole school organized by Jarah Evslin, and I am partially taking care of Croatia related issues (visa, trasnportation advice. communication to the owners of the housing). Lots of interesting things here about star formation, black hole formation, making massive black holes from lighter ones and so on. And some string theory mechanisms related to black hole entropy and similar issues. Most of people are postdocs and students here. Among seniors, Holger Nielsen and Mina Aganagić are present to our benefit.
By the way, started a stub black hole. Please contribute.
started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective
am finally splitting this off from Hopf invariant
I have added at HomePage in the section Discussion a new sentence with a new link:
If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.
I had completly forgotton about that page Welcome to the nForum (nlabmeta). I re-doscivered it only after my recent related comment here.
Created:
Just like an ordinary scheme in algebraic geometry is glued from affine schemes, a C^∞-scheme in differential geometry is glued from smooth loci.
The original reference is
See the artice C^∞-ring for more references.
starting something.
I claim that in terms of quantum circuits via dependent linear types, the principle of deferred measurement is immediately formalized and proven by the Kleisli equivalence:
Namely a quantum circuit involving measurement in the B-basis anywhere is a Kleisli morphism Circ:ℋ≔□Bℋ•⟶ℋ• for the linear necessity-comonad, and the Kleisli equivalence says that this equals a coherent (non-measurement) quantum circuit δ□∘□Circ:ℋ→ℋ postcomposed with the □-counit: But the latter is the measurement gate.
Change 1: Original page describes the fan theorem as requiring the bar to be decidable, claims that the “classical” fan theorem contradicts Brouwer’s continuity principle. The latter claim is not true; I corrected the error. I have stated the result as two separate theorems: the decidable fan theorem, about decidable bars, and the fan theorem, about bars in general.
Change 2: Slightly more information is provided about the relationship between the Fan Theorem and Bar Induction. Eventually, we should make a page about the latter.
Change 3: the section on equivalents to the fan theorem has been fixed somewhat. The section originally asserted that all of the statements provided were equivalent to the decidable fan theorem; in fact, some are equivalent to the decidable fan theorem and some to the full fan theorem.
moving material about the weak limited principle of omniscience from principle of omniscience to its own page at weak limited principle of omniscience
Anonymouse
added pointer to yesterday’s
added doi-link to
this is a bare subsection with a list of references, meant to be !include-ed into the References-lists of relevant entries (such as AdS-QCD correspondence, AdS-QCD correspondence but also at flux tube and maybe at string)
added some references on constructive analysis here.
I have expanded a bit at Serre-Swan theorem: gave it an actual Idea-section, mentioned more variants (over general ringed spaces, in higher geometry) and added more references.
New article class equation, just to fill some gaps in the nLab literature. Truly elementary stuff.
New page: monadic decomposition.
this page needs attention. For the moment I have at least added these original articles:
Michael Atiyah, Isadore Singer, Index theory for skew-adjoint Fredholm operators, Publications Mathématiques de l’IHÉS, Tome 37 (1969) 5-26 [numdam:PMIHES_1969__37__5_0]
Max Karoubi, Espaces Classifiants en K-Théorie, Transactions of the American Mathematical Society 147 1 (Jan., 1970) 75-115 [doi:10.2307/1995218]
added pointers:
For superconformal field theory, such as D=4 N=1 SYM, D=4 N=2 SYM, D=4 N=4 SYM, D=6 N=(1,0) SCFT, D=6 N=(2,0) SCFT:
Christopher Beem, Madalena Lemos, Pedro Liendo, Leonardo Rastelli, Balt C. van Rees, The N=2 superconformal bootstrap (arXiv:1412.7541)
Christopher Beem, Madalena Lemos, Leonardo Rastelli, Balt C. van Rees, The (2,0) superconformal bootstrap (arXiv:1507.05637)
Christopher Beem, Leonardo Rastelli, Balt C. van Rees, More N=4 superconformal bootstrap (arXiv:1612.02363)
Wrote a section on the associated monad at operad, in terms of the framework introduced under the section titled Preparation.
I am splitting off Zariski topology from Zariski site, in order to have a page for just the concept in topological spaces.
So far I have spelled out the details of the old definition of the Zariski topology on 𝔸nk (here).
added to Lie algebra a brief paragraph general abstract perspective to go along with this MO reply
Made some edits and additions at simplicial complex.
just to make links work, I have started a minimum at gravitational wave.
tried to bring the entry orientation into a bit of shape
I expanded Maxwell’s equations by adding the integral form in SI system and then a shorter version of discussion from electromagnetism for the differential form of the equations, both in 3d and 4d formulations. Note also that Ampère’s law is about producing magnetic field from current; while it is Maxwell’s equation, or Ampère-Maxwell which adds the term with the change of electric field, the main discovery of Maxwell. Some people nowdays say generalized Ampère’s law what I wrote, but I am not happy about it as the general form does not generalize it in the straightforward manner, but adds new physics what needs a separate attribution.
I noticed only now that the entry bimodule is in bad shape and needs some attention. For the moment I have added here a mentioning of the 2-category of algebras, bimodules and intertwiners and a pointer to the Eilenberg-Watts theorem.
Todd, thanks for this interesting entry (colimits in categories of algebras)! I left a query box describing a possible simple proof for the last theorem using the adjoint lifting theorem (I hope there are no substantial errors).
at additive functor there was a typo in the diagram that shows the preservation of biproducts. I have fixed it.
Also formatted a bit more.
a stub, for the moment just so as to record pointer to Simpson 12 where “resolution of the paradox” is claimed to be achieved simply by passing from topological spaces to locales
I have added a comment and collected some references on the renormalization freedom in the cosmological constant: here
I have cross-linked this with related entries: renormalization, perturbative quantum gravity and stress-energy tensor
in order to satisfy links, but maybe really in procrastination of other duties, I wrote something at quantum gravity
Added more material to Boolean algebra, particularly the principle of duality and the connection to Boolean rings, and a wee bit of material on Stone duality.
Stone duality deserves greater expansion, bringing out the dualities via ambimorphic (ahem, schizophrenic) structures on the 2-element set, and mentioning the connection to Chu spaces. Another day, another dollar.
I am giving this bare list of references its own entry, so that it may be !include-ed into related entries (such as topological quantum computation, anyon and Chern-Simons theory but maybe also elsewhere) for ease of updating and synchronizing
I’ll be working a bit on supersymmetry.
Zoran, you had once left two query boxes there with complaints. The second one is after this bit of the original entry (this will change any minute now)
The theory of supergravity is, as a classical field theory, an action functional on functions on a supermanifold X which is invariant under the super-diffeomorphism group of X.
where you say
Zoran: action functional is on paths, even paths in infinitedimensional space, but not on point-functions.
I think you got something mixed up here. If X is spacetime, a field on X is the “path” that you want to see. The statement as given is correct, but I’ll try to expand on it.
The second complaint is after where the original entry said
many models that suggest that the familiar symmetry of various action functionals should be enhanced to a supersymmetry in order to more properly describe fundamental physics.
You wrote:
This is doubtful and speculative. There are many models which have supersymmetry which is useful in their theoretical analysis, but the same models can be treated in formalisms not knowing about supersymmetry. Wheather the fundamental physics needs a model which has nontrivial supersymmetry is a speculative statement, and I disagree with equating theoretical physics with one direction in “fundamental physics”. I do not understand how can a model suggest supersymmetry; it is rather experimental evidence or problems with nonsupersymmetric models. Also one should distinguish the supersymmetry at the level of Lagrangean and the supersymmetry which holds only for each solution of the equation of motion.
I’ll rephrase the original statement to something less optimistic, but i do think that supersymmetry is suggsted more by looking at the formal nature of models than by lookin at the nature of nature. If you have a gauge theory for some Lie algebra (gravity, Poincaré Lie algebra) and the super extension of the Lie algebra has an interesting classification theory (the super Poincar´ algebra) then it is more th formalist in us who tends to feel compelled to investigate this than the phenomenologist. Supersymmetry is studied so much because it looks compelling on paper. Not because we have compelling phenomenological evidence. On the contrary.
So, if you don’t mind, I will remove both your query boxes and slightly polish the entry. Let’s have any further discussion here.
Added to group object the Yoneda-embedding-style definition and added supergroup to the list of examples.
Corrected typo (“Wikiedpia” to “Wikipedia”). Also added pentagon decagon hexagon identity as related entry.