As there had been a change to the entry for Ross Street I gave it a glance. Is there a reason that the second reference is to a paper without Ross as an author?I hesitate to delete it as there may be a hidden reason. (I have edited this discussion entry to remedy the point that Todd and Urs have made below. I also edited the title of this discussion!)

]]>I needed a redirect-kind of entry *ordinary homology*. So I created one.

added pointer to:

- Georges de Rham, Chapter V of:
*Differentiable Manifolds – Forms, Currents, Harmonic Forms*, Grundlehren**266**, Springer (1984) [doi:10.1007/978-3-642-61752-2]

added pointer to:

- Georges de Rham, Chapter III of:
*Differentiable Manifolds – Forms, Currents, Harmonic Forms*, Grundlehren**266**, Springer (1984) [doi:10.1007/978-3-642-61752-2]

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

]]>Created a stub for the conference.

]]>added to *modular form* a brief paragraph with a minimum of information on modular forms *As automorphic forms*. Needs to be expanded.

Where the page has

The index theorem is supposed to have an interpretation in terms of the quantum field theory of the superparticle on the given space,

is the “is supposed to” necessary? Why not “has an interpretation”? Is it just the general issue of any translation from mathematics to physics?

]]>a bare list of references, to be `!include`

-ed into relevant entries, such as at *elliptic cohomology*, but also at *equivariant elliptic cohomology*, *elliptic genus*, *Witten genus* etc.

(in an attempt to clean up and harmonize the referencing across all these entries – still some way to go towards that goal, but it should be a start)

]]>I started an entry at nucleus of a profunctor. Much more could be said, including plenty of examples. I don’t know what people think about splitting examples into those where the profunctor is Hom from the rest.

Do we not already have something on the ’center of an adjunction’, perhaps under a different name?

We have Legendre transfomation already. Is there a standard way to take the Legendre-Fenchel transform as a generalization?

]]>I have added very briefly a disambiguation line to the top of the entry genus. But eventually I guess we may need a genuine disambiguation page.

]]>I have given *external tensor product* its own entry.

What I would really like to do for the moment is record there sufficient conditions under which the fiber over $X_1 \times X_2$ is *generated* from external tensor products. I have added two references that discuss this for quasicoherent sheaves, but otherwise there is no discussion yet. Am being interrupted now.

(What I really want eventually is conditions such that $Mod(X_1 \times X_2) \simeq Mod(X_1) \otimes_{Mod(\ast)}Mod(X_2)$)

]]>I have split off from *differential form* an entry *integration of differential forms*, without much ado. Maybe to be polished later…

Add a stub, since this concept has been referenced on other pages.

]]>added these pointers:

Victor Buchstaber,

*The Chern–Dold character in cobordisms. I*,Russian original: Mat. Sb. (N.S.), 1970 Volume 83(125), Number 4(12), Pages 575–595 (mathnet:3530)

English translation: Mathematics of the USSR-Sbornik, Volume 12, Number 4, AMS 1970 (doi:10.1070/SM1970v012n04ABEH000939)

Victor Buchstaber, A. P. Veselov,

*Chern-Dold character in complex cobordisms and abelian varieties*(arXiv:2007.05782)

created *Hodge structure*. Currently with nothing but a pointer to this nice book:

- Chris Peters, Jozef Steenbrink,
*Mixed Hodge Structures*, Ergebisse der Mathematik (2007) (pdf)

Eventually I’d think we should move over Hodge-structure articles from *Hodge theory* to here. But not tonight.

wrote out the definition *In complex geometry*

I am trying to collect citable/authorative references that amplify the analog of the mass gap problem in particle phenomenology, where it tramslates into the open problem of computing hadron masses and spins from first principles (due to the open problem of showing existence of hadrons in the first place!).

This is all well and widely known, but there is no culture as in mathematics of succinctly highlighting open problems such that one could refer to them easily.

I have now created a section *References – Phenomenology* to eventually collect references that come at least close to making this nicely explicit. (Also checked with the PF community here)

This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:

In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.

Here are examples:

A

*quiver*is just a directed graph (pseudograph, to be explicit). But one says*quiver*instead of*directed graph*when one is interested in studying*quiver representations*: functors from the free category on that graph to the category of finite-dimensional vector spaces.A

*presheaf*is just a contravariant functor. But one says*presheaf*instead of*contravariant functor*when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.

(…)

]]>added pointer to:

Nomaan X,

*Quantum Field Theory On Causal Sets*, in*Handbook of Quantum Gravity*, Springer (2023) [arXiv:2306.04800]Stav Zalel,

*Covariant Growth Dynamics*, in*Handbook of Quantum Gravity*, Springer (2023) [arXiv:2302.10582]

starting a `category:reference`

-page in which to eventually collect pointers to the contributions to this upcoming book collection

am finally giving this its own entry. But for the moment there is just a brief Idea-section and a list of references.

]]>starting discussion page

Anonymous

]]>started a minimum at *writer comonad*