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added to Jones polynomial pointers to Edward Witten’s slides for his recent talks at the Clay meeting in Oxford.
Thanks to Bruce Bartlett for providing them!!
starting something, to record Prop. 7.6 in
still need to add details – not done yet
added this pointer on the relation of the colored Jones polynomial to Lie algebra weight systems on chord diagrams:
added this pointer:
starting something; for the moment just to go with BTZ black hole
brief category:people
-entry for hyperlinking references at BTZ black hole
am splitting this off from hyperbolic manifold, in order to clean up a little
created in order to record this recent article:
Hi all, I added an entry for Leibniz’s identity of indiscernibles.
I thought it would be nice to include a discussion of the way in which univalence refines the identity of indiscernibles, but I am just beginning to learn about UF and was not sure what to say.
In Awodey’s 2013 exposition of univalence he states:
“Rather than viewing it as identifying equivalent objects, and thus collapsing distinct objects, it is more useful to regard it as expanding the notion of identity to that of equivalence. For mathematical purposes, this is the sharpest notion of identity available; the question whether two equivalent mathematical objects are “really” identical in some stronger, non-logical sense, is thus outside of mathematics.”
Thus we can regard univalence as “loosening” the notion of identity in such a way that it validates Leibniz’s law.
Certainly, I can just add something like this. However, it seems to me that a philosophical notion of equality that accords with intuition may profitably make a distinction between isomorphic structures when they are not “really” equal ontologically. Awodey is making a stance about “mathematical” rather than “real” identity, as is considered in (some formulations?) of Leibniz’s Law.
Is it possible to think about the connection to Leibniz’s Law like this:
Equivalence is akin to and entails a kind of “observational equivalence”/indiscernibility.
Thus we have the following putative principles:
So can we think of Univalence as a refinement that says “Indiscernibility is indiscernible from identity, so we may as well treat indiscernibles as equal by transporting isomorphisms into identifications.”? Or is this not the way to think about this/do folks in UF have a stronger stance such as “real” equality being absurd?
Best, Colin
I should say – for those watching the logs and wondering – that I started editing the entry global equivariant homotopy theory such as to reflect Charles Rezk’s account in a coherent way.
But I am not done yet. The entry has now some of the key basics, but is still missing the general statement in its relation to orbispaces. Also some harmonizing of the whole entry may be necessary now, as I moved around some stuff.
So better don’t look at it yet. I hope to bring it into shape tomorrow or so.
(In the process I have split off global orbit category now.)
added a bunch of further links, and made Dmitry Volkov a redirect
For hyperlinking references in the History-section st supergravity
brief category:people
-entry for hyperlinking references at DBI action
Added a reference:
brief category:people
-entry for hyperlinking references at Chern-Simons Wilson lines in AdS3-CFT2 – references and at 3d gravity
brief category:people
-entry for hyperlinking references at Chern-Simons Wilson lines in AdS3-CFT2 – references
To record today’s
added pointer to
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.
And now I’ve started Dehn surgery. Be warned however that there may be inaccuracies, or it may be amateurish.
an entry listing references on the classification of possible long-range forces, hence of scattering processes of massless fields, by classification of suitably factorizing and decaying Poincaré-invariant S-matrices depending on particle spin, leading to uniqueness statements about Maxwell/photon-, Yang-Mills/gluon-, gravity/graviton- and supergravity/gravitino-interactions.
This is to be !include
-ed in the References-section of other entries, therefore no further material here
I have moved a Properties-section to strict n-category, taken from (infinity,n)-category (where it serves as a preliminary), which collects the statements from section 2 of Barwick&Schommer-Pries (see the refereces there).
Just to be clear, if at wrapped cycle is a multiple of a cycle , would we or wouldn’t we say it wrapped it?
brief category:people
-entry for hyperlinking references at AdS3-CFT2 and CS-WZW correspondence
I finally learned about the general abstract story behind the notion of orientation in -cohomology, for an -ring, in terms of trivialization of -associated -bundles – from this lecture by Mike Hopkins
I added some remark about that to orientation in generalized cohomology. Needs more polishing and expansion, but I have to interrupt for the moment.
I thought this should be better developed, and it is. Following the work of Sundholm and Ranta, several people are trying to use dependent type theory to understand natural language. This involves a range of things philosophers care about: anaphora, polysemy, modality, factivity, etc.
It should be interesting to bring this work into contact with the work here on dependent type theory in mathematics and physics. Already I see an overlap in the analysis of modality via a type of worlds, between us here and them in Resolving Modal Anaphora in Dependent Type Semantics on p. 89.
So I’ve started a page dependent type theoretic methods in natural language semantics to list references, and later results.
cross-linked with single trace observables, copied over the relevant paragraphs from there to a new section here: Via single trace observables under AdS/CFT
I gave the entry super vector space some expositional background and a more detailed (pedantic) definition.
starting a small entry here, for ease of hyperlinking. This is to go along with metric Lie algebra
am splitting this off from n-Lie algebra (which should better be renamed to Filippov algebra)
– am being interrupted now – not done yet…
brief category:people
-entry for hyperlinking (at Faulkner construction, presently redirecting to M2-brane 3-algebra) this reference:
(I hope I have identified the author’s webpage correctly – if anyone knows, please check)
added some actual text to the category:people entry Roger Penrose
I was looking for a place to record a somewhat more global overview of the notion of locally presentable category, its related notions and its generalizations to higher category theory. But somehow all of the existing entries feel too narrow in focus to accomodate this. So I ended up creating now a new entry titled
Think of this as accomodating material such as one might present in a seminar talk that is meant to bring people with some basic background up to speed with the relevant notions, without going into the wealth of technical lemmas.
I only just started. Will continue in a moment after a short break…
brief category:people
-entry for hyperlinking references at M2-brane 3-algebra