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    • I have added pointer to Mike’s discussion of spectral sequences here at “homotopy spectral sequence” and in related entries.

      But now looking at this I am unsure what the claim is: has this been formalized in HoTT?

      (Clearly a question for Mike! :-)

    • expanded the entry cofinal functor: formal definition, list of equivalent characterizations and textbook reference.

    • Hi guys and girls,

      I have set up a new subject on the nlab, related to the previously opened subject of global Hodge theory:

      http://ncatlab.org/nlab/show/Arithmetic+cryptography

      Contributions are welcome (in particular to fill-in the blanc subjects on this page, if you like).

      Fred
    • Hi guys,

      I plan to improve drastically the content of the nlab on Hodge theory, p-adic, classical and global.

      With this perspective in mind, i have made some new topics, and improved the section on global analytic geometry, by adding in particular a new reference of mine that contains a notion of strict global analytic spaces and some perspectives for its use to study various problems of arithmetic geometry.

      The new topics, that should be the place to discuss these subjects if you are interested, are: generalized Lambda-structures and global Hodge theory. I also plan to make a page on special values of L-functions, and another on the spectral interpretation of zeroes and poles of L-functions.

      I don't connect often to the nforum, so i may not discuss a lot about the present message, but the nlab pages will be updated. Contact me by email at frederic.paugam@imj-prg.fr if you would like to discuss these things.

      All the best,

      Frédéric

    • How would you define the usual jargon “fragment” in logic?

      There ought to be a simple formal definition, I suppose, such as “Given a language L and a theory T in that language, then a fragment of T is… “

    • Discussion with Mike reminded me that we were lacking an entry reflective subuniverse.

      I started a template and cross-linked, but now I am out of battery and time before filling in any content. Will do that tomorrow.

    • This is to flag up two entries that so-far just have titles. They are IulianUdrea and perfectly normal space. These may need watching. The second may be ok, and be a page somone has just started and intends to continue, but the name on the second also occurs as a name on a Mo page with no questions and no answers and may be someone seeing how many wikis etc they can put stuff on! Sorry for being a nasty suspicious b*****, but it looks a bit strange to me.

      (N.B., the two entries do not seem to be related.)

    • at diffeomorphism I started listing theorems and references on statements about when the existence of a homeomorphism implies the existence of a diffeomorphism.

      I dug out ancient references for the statement that in d≠4d \neq 4 everything homeomorphic to an open dd-ball is also diffeomorphic to it. What would be a more modern, more canonical, more textbook-like reference for this?

      And I’d also like to cite a reference for what is maybe obvious, that if that something in d=4d = 4 is an open subset of ℝ 4\mathbb{R}^4 equipped with the induced smooth structure of the standard smooth structure, then the statement is also true in that dimension.

      In fact, I am looking for nice/explicit/useful diffeomorphisms from the open nn-ball onto the open nn-simplex. I can of course fiddle around and cook up something, but I haven’t found anything that would count as nice. But probably some engineer out there working with finite elements or something does have a convenient choice.

    • there is this new master thesis:

      • Cesare Gallozzi, Constructive Set Theory from a Weak Tarski Universe, MSc thesis (2014)

      which discusses aspects of weak Tarskian homotopy type universes following the indications that Mike Shulman has been making, for instance at universe (homotopytypetheory). I just got permission to share this and I have now included pointers to the thesis to that entry, to type of types, etc.

    • At some point I had made up the extra axiom/terminology saying that an object 𝔸 1\mathbb{A}^1 in a cohesive ∞\infty-topos “exhibits the cohesion” if the shape modality is equivalent to 𝔸 1\mathbb{A}^1-localization. Now I was talking about that assumption with Mike and noticed that this didn’t have a reflection on the nnLab yet.

      So now I have added, for the record, the definition here at “cohesive oo-topos” and cross-linked with the existing discussion at “continuum”.

    • added recent AlgTop mailing list contribution on fibrant replacement of cubical sets to cubical set

    • I added to (infinity,n)-category of cobordisms a description in plain English (or what I make of that...) of Lurie's definition of Bord_{(\infty,n)}.

      The definition is very simple and elegant, but it is not being exposed really in Lurie's writeup, and the whole definition 2.2.9, which is central to the article, is itself rather hidden somewhere, so I I am making the experience that people staring at the document tend not to see the simple point here. As a reaction to that, I thought I'd write this out now.
    • I added the definition of funcoid in nLab wiki.

      I also call the theory of funcoids "Algebraic General Topology" because it somewhere replaces epsilon-delta notation with more algebraic formulas.

      Feel free to copy more materials about funcoids, reloids, and their generalizations from my site to nLab.

      The theory of funcoids is very productive in creating new open problems and research trends. I welcome to work with me. Read the manuscripts at my site.

    • I’ve written a stub on Cole’s theory of spectrum which for the time being consists largely of references and links. Further curation or correction would be appreciated!

    • David Mumford has a treasure trove of free material at his website, so I added a link to his page.

    • Flattered though I was at being promoted to an n-category cafe author, I had to change 'Roberts' to 'Corfield' at Online resources in the description of our favourite stomping ground. Someone's fingers got the better of them, I didn't look who ^_^

      -David Roberts

    • I have added several historically important references at space-time.

    • I did a bit of editing (of Definition and Examples) at child’s drawing (once known as children’s drawing), to emphasize that a child’s drawing/dessin d’enfant is not simply a hypermap, but (typically) a hypermap seen as the representation of a Belyi function. I was guided by the presentation in Lando & Zvonkin 2004 (this paper by Zvonkin is also helpful), but apologies if I introduced any mistakes since I’m just learning this stuff.

    • Few references collected as a start of entry spectrum of a graph redirecting also Ihara zeta function, prompted by today’s remarkable paper by Huang and Yau and thereby revived memory of a colloqium talk by Bass in which I enjoyed at University of Wisconsin in late 1990s.

    • added to group completion a paragraph with minimum pointers to the traditional construction ΩB(−)\Omega B (-) as group completion of topological monoids. Added a corresponding brief paragraph to K-theory of a permutative category (where this had been missing).

      What is still missing (on the nnLab and maybe generally in the literature) is a really clear statement that this is indeed a model for the ∞\infty-categorical group completion operation which is invoked at K-theory of a symmetric monoidal (infinity,1)-category.

      One place where such a derived functor statement is made is Dwyer-Kan 80, remark 9.7 (thanks to Charles Rezk’s MO comment here). I have added pointers to that to the relevant entries, but this ought to be sorted out in more detail.

    • What mathematicians call the Mellin transform relating a theta function to its (completed) zeta function

      ζ^(s)=∫ 0 ∞t s−1θ^(t)dt \hat \zeta(s) = \int_0^\infty t^{s-1} \hat \theta(t) \, d t

      is precisely what physicists call the Schwinger parameter-formulation which takes the partition function of the worldline formalism to the zeta-regulated Feynman propagator

      TrH −s=∫ 0 ∞t s−1Trexp(−tH)dt. Tr H^{-s} = \int_0^\infty t^{s-1} Tr \exp(- t H) \, d t \,.

      I have tried to briefly mention this relation in relevant entries and to cross-link a bit. But more should be done.

    • I created a stub on Sam Gitler who has recently died. He was very important not only for his contribution to Yang-Mills theory and the Brown-Gitler spectrum, but also for his creation, with Adem of the school of algebraic topology in Mexico. (I have changed all the mentions of Gitler to be ‘active’.)

    • I have not yet made this change – as a newbie, I want to get an opinion first.

      associative unital algebra describes an RR-algebra AA, for RR commutative, as a “ring under RR”. From under category, this is just an object in the coslice category R↓RingR \downarrow \operatorname{Ring}: a map R→AR \to A, where AA is another ring. However, I believe that such a map gives an RR-algebra only if its image is in the center of AA (for example, Wikipedia). I’m not sure how to fix that. Maybe we should just remove the “under RR” item from that first page. Thoughts?

    • since the story of the various duals, compactifications and twists of gauge field theories which constitute “Witten’s grand story” (or whatever it should be called in total) gets a bit long, I thought it would be good to have a birds-eye view digest of it – and so I created a survey table

      gauge theory from AdS-CFT – table

      and included it into some relevant entries.

      (There is clearly still room for expansion and further details, but maybe it’s a start).

    • finally created a minimum at Dirichlet theta function, cross-linked with Dirichlet character and Dirichlet L-function and added it to the table (bottom left entry)

      (I have gotten a funny problem with my Opera browser having trouble loading nLab pages. Something makes it choke. For instance when I try to edit a page it tends to show me a blank screen, but when I then go to edit the same page with another browser, then that informs me that the page is locked, so Opera did get to that point, but then got stuck. This happens since the last few days. I tried clearing caches, but it didn’t seem to help. Hm. )

    • Someone set up a new page with title www.fuw.edu.pl/~slworono/PDF-y/OP.pdf. It seems that this is an attempt by Stanisław Lech Woronowicz to create a nlab entry. Should we just convert it to a usual format page for him? The pdf file is a copy of his paper:Operator theory in the C *C^*-algebra framework., joint with K.Napi ́orkowski.

    • Added a stub at Waldhausen K-theory of a dg-category. I call this the Waldhausen K-theory and not simply K-theory because I imagine that there should also be a more intrinsic definition not passing through Waldhausen categories or stable infinity-categories.

    • started some minimum at vacuum amplitude. Briefly mentioned relation to a) generating functionals for correlators and b) to zeta functions and c) to expected evanishing in supersymmetric theories

      Remarked that in view of b) and c) one is tempted to expect some relation between 1-loop vacuum amplitudes of supersymmetric field/string theories with the Riemann hypothesis. Added a pointer to the article ACER 11 which seems to find just that.

      If anyone has further pointers to literature relating vanishing of susy 1-loop vacuum amplitudes and (generalized) Riemann hypotheses, please drop me a note.

    • started some minimum at vacuum energy, but running out of battery now.

    • This here to collect resources on the observation that – in view of pertinent arithmetic/differential-geometry analogies – an Artin L-function of a Galois representation looks like the zeta function of a Laplace operator of a Dirac operator twisted by a flat bundle.

      I currently see this in the literature in three steps:

      1. the Selberg zeta function, which is originally defined as some Euler product, is specifially equal to an Euler product of characteristic polynomials (just as the Artin L-function). This turns out to be due to Gangolli77 and Fried86, and I have collected these references now at Selberg zeta function – Analogy with Artin L-function with a cross-linking paragraph also at Artin L-function itself

      2. more specifically, those characteristic polynomials are those of the monodromies/holonomies of the given group representation, regarded as a flat connection. This is prop. 6.3 in Bunke-Olbrich 94.

      3. finally, that product over characteristic polynomials of monodromies is indeed the zeta function of the bundle-twisted Laplace operator. This is the main point in Bunke-Olbrich 94, somehow, but I still need to fiddle with extracting a more explicit version of this statement.

    • I made a start on regular representation (via a stub from normalizer). My first thought was to made this a generic regular representation page so I put in definitions for groups and algebras.

      Once I’d created the page I thought that it could be said to be an example of a more general thing whereby a monoid acts on itself. However, someone’s already editing the page (that was fast!) so I’ll have to wait to put that in.

      (Unless the anonymous coward reads this and decides to put it in themselves!)

    • Some time ago I started a stub characteristic variety to record few references, mainly in D-module context. Regarding that the related notion of a characteristic ideal also appears in the treatment of Iwasawa polynomial and Alexander polynomial which Urs wants to understand from the point of view of connections and differential refinements of cohomology, maybe we should do some effort to make some pages which will connect various notions of characteristic ideals and their loci across various subjects. I just recorded

      • Andrea Bandini, Francesc Bars, Ignazio Longhi, Characteristic ideals and Iwasawa theory, arxiv/1310.0680; Characteristic ideals and Selmer groups, arxiv/1404.2788

      at characteristic ideal for the version in the context of Iwasawa theory.

    • In some thread here (which I seem to have lost) there was the open question of whether the Selberg zeta function is indeed the zeta function of the corresponding Laplace operator. The answer is of course Yes, I have added the following paragraph to zeta function of a Riemann surface:

      That the Selberg zeta function is indeed proportional to the zeta function of a Laplace operator is due to (D’Hoker-Phong 86, Sarnak 87), and that it is similarly related to the eta function of a Dirac operator on the given Riemann surface/hyperbolic manifold goes back to (Milson 78), with further development including (Park 01). For review of the literature on this relation see also the beginning of (Friedman 06).

      (the links will only work from within the entry)

    • gave Langlands correspondence an actual Idea-section.

      (Am in a rush and on a horrible wifi connection. Need to proof-read and add more links later.)

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