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Supergravity BPS Charges, that's is the topic of the next session of the Higher Cartan Geometry Seminar [1]. Lecture notes are at [2].

[1] http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
[2] http://ncatlab.org/nlab/show/geometry+of+physics+--+BPS+charges

Consider (X,g) a super-spacetime and ω a degree (p+2)-differential form on X which is a WZW curvature form definite on the super Lie algebra cocycle for Green-Schwarz super p-brane sigma model with target space X. Then the Polyvector extensions of the super Lie algebra of super-isometries of (X,g) by charges Z of Noether currents of the super p-brane sigma model are known as algebras of BPS charges. (The spacetime (X,g,ω) is called a supergravity 1/k-BPS state if the dimension of the space of supercharges Q in the kernel of the above bracket is 1/k-th of that of super Minkowski spacetime).

This is well understood in the literature (Azcárraga-Gauntlett-Izquierdo-Townsend 89) for the case that X is locally modeled on an ordinary super Minkowski spacetime and that the p-brane species is in the old brane scan (e.g the type II superstrings, the heterotic superstring and the M2-brane, also e.g. the super 1-brane in 3d and the 3-brane in 6d, but not the D-branes and not the M5-brane).

For the full story of string theory this needs to be refined in three ways (see Fiorenza-Sati-Schreiber 13), and this has been left open in the literature, for previous lack of a higher differential geometry that could handle this:

1. For a genuine global definition of the Green-Schwarz super p-brane sigma model with target (X,ω), the WZW curvature form ω needs to be prequantized to a globally well-defined WZW term, a genuine cocycle in Deligne cohomology (a circle (p1+1)-bundle with connection).

(The need for this has broadly been ignored, one place where it is mentioned is (Witten 86, p. 17).)

2. For the inclusion of p2-brane charges of p2-branes on which p1-branes may end (for p1=1: type II strings ending on D-branes, for p1=2 and p2=5 M2-branes ending on M5-branes) then X is to be locally modeled on an extended super Minkowski spacetime, hence on a super orbispace, hence a curved spacetime now is an object in higher Cartan geometry and one needs to make sense of Noether currents there.

(Arguments in this direction for the D-branes have been given in (Hammer 97) and for the M5-brane in (Sorokin-Townsend 97).)

3. For inclusion of non-infinitesimal isometries one needs the global structure of the full supergroup of BPS charges, not just its super Lie algebra.

Here we discuss how to solve these problems in full generality. Specified to the situation in 11-dimensional supergravity with M2-branes and M5-branes we find that the BPS charges traditionally seen in the M-theory super Lie algebra as living in ordinary cohomology H5(X)⊕H2(X) receive corrections by d4-differentials of a Serre spectral sequence given by cup product with the class of the supergravity C-field. This is in higher analogy to how D-brane charges are well known (Maldacena-Moore-Seiberg 01) to be in ordinary cohomology only up to corrections of the d3-differential (and higher) in an Atiyah-Hirzebruch spectral sequence for twisted K-theory,given by cup product with the class of the B-field. This supports the conjecture (Sati 10) that M5-brane charge should really be in twisted elliptic cohomology, since this is what is canonically twisted by these degree-4 classes (Ando-Blumberg-Gepner 10). (Realizing this fully amounts to refining the M5-WZW term that we construct in ordinary differential cohomology below to ellitptic differential cohomology. Discussion of that refinement is beyond the scope of this page here.)

We also close a gap in (AGIT89): what is strictly derived there from the Noether theorem is extension of the supersymmetry algebra by differential forms, while the argument that it is only the de Rham cohomology class of these forms that matters relies on physics intuition. We find here that the Lie algebra of conserved currents extending the (super)isometry algebra is naturally not just a (super)Lie algebra but a (super)Lie (p+1)-algebra including higher order symmetries of Noether symmetries. It is by quotienting these out when restricting the current Lie n-algebra to its lowest Postnikov stage that current forms pass to their de Rham equivalence classes. Accordingly, the fully globalized current groups that we find are really (super)smooth n-groups. For instance the M-theory super Lie algebra is refines to a super Lie 6-group, where 6=5+1 is the dimension of the M5-brane worldvolume.

http://ncatlab.org/nlab/show/geometry+of+physics+--+BPS+charges
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Differential equations are coalgebras of the jet co-monad. This statement appeared in full beauty in [1]

Michal Marvan, "A note on the category of partial differential equations", in Differential geometry and its applications, Proceedings of the Conference in Brno August 24-30, 1986,

The Kleisli category of course is a full subcategory of that, and the statement about differential operators being co-Kleisli morphisms of the jet comonad that I asked for before [0] is the special case of the above made fully explicitly in [2]

Michal Marvan, section 1.1 of "On Zero-Curvature Representations of Partial Differential Equations", 1993

Now since this statement about differential operators is true, of course every other true statement about differential operators that one finds elsewhere in the literature will be compatible with it, but Marvan is the only author I am aware of who explicitly states the neat general abstract statement that I asked for. It's one of those abstract trivialities, if you wish, that are worth making explicit.

On the other hand, Marvan checks that Jet is a comonad directly, without realizing it as the base change comonad along the unit of the de Rham stack monad iX:X→XdR. For that statement of course one needs to be in a model of synthetic differential geometry in order for XdR to exist, such as (but not necessarily) algebraic geometry.

In the algebraic context, the reference stating this explicitly  that I am aware of is [3]

Jacob Lurie, above prop. 0.9 of "Notes on crytsals and algebraic D-modules", 2009

Here it is maybe noteworthy that from this it follows immediately that the Jet-comonad is right adjoint to the "infinitesimal disk bundle" monad Tinf.

This adjunction (Tinf⊣Jet) itself, without however its origin in the base change adjoint triple  was observed in the context of synthetic differential geometry in [4]

Anders Kock, above prop. 2.2 of "Formal manifolds and synthetic theory of jet bundles", 1980

I'll just add that one immediate neat implication of making the general abstract comonad theory behind this explicit is that it gives in full generality that for any topos (or ∞-topos) H equipped with an "infinitesimal shape modality" X↦IX=XdR, then since Jet is a right adjoint, a standard fact (here for toposes, here maybe for ∞-toposes) gives that its EM-category, hence the category PDE(X) of PDEs in X is itself a topos, sitting by a geometric morphism

PDE(X) → H/X

over H, whose inverse image is (non-fully) that co-Kleisli category of bundles over X with differential operators between them.

Now moreover, using the infinitesimal shape modality I it also follows that on H/X there is an étalification coprojection Et (here). This is such that when E∈H is a coefficient for a differential cohomology theory (e.g. any stable object in the case that H is cohesive (here)), then Et(X∗E) has the interpretation of being the "bundle of E-connections" over X. So with the above geometric morphism we may transfer all this to the topos PDE(X) along the composite

ι:H → H/X → H/X → PDE(X).

Unwinding what this all means, in view of Marvan's insight above, it follows, I think, that for any bundle F∈H/X→PDE(X) then maps in PDE(X) of the form

F→ ιE
are equivalently horizontal "E-differential forms" on the jet bundle of F, in the sense of variational bicomplex theory.

That might count as some non-trivial mileage gained out of making explicit the statement that I was asking for.

[0] https://plus.google.com/+UrsSchreiber/posts/1nCuqkvnsxN
[1] http://ncatlab.org/nlab/show/jet%20comonad#Marvan86
[2] http://ncatlab.org/nlab/show/differential+operator#Marvan93
[3] http://ncatlab.org/nlab/show/jet+bundle#Lurie
[4] http://ncatlab.org/nlab/show/infinitesimal%20disk%20bundle#Kock80
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Thank you so much!

I would be very grateful if you could also comment these lines "The ordinary pure 3D Chern-Simons theory is topological – observables only depend on the spacetime (or world volume) topology – so it's of course exactly conformal, too. When one adds matter, the theory ceases to be topological but with some good choices, it may stay conformal." from http://physics.stackexchange.com/a/28769 and "Topological quantum field theory is one that contains no excitations that may propagate "in the bulk" of the spacetime so it is not appropriate to describe any waves we know in the real world. The characteristic quantity describing a spacetime configuration - the action - remains unchanged under any continuous changes of the fields and shapes. So only the qualitative, topological differences between the configurations matter." from http://physics.stackexchange.com/a/19780/74563

These lines above seem kind of wrong to me: I'm trying to compare them with what you wrote in the very interesting article http://arxiv.org/abs/1408.0054 and in your answer http://physics.stackexchange.com/a/98384/74563, for instance "the case of extended topological QFT (where the manifolds are equipped only with smooth structure) is entirely defined and classified by a universal construction in directed homotopy theory, i.e. (∞,n)-category theory" or "This includes topological objects as well as smooth ones, and also variants of differential geometry such as supergeometry, which is necessary for a full treatment of quantum field theory (for the description of fermions).", etc... "Generally, this is what the foundation of physics in higher geometry/higher topos theory/homotopy type theory is all about...", etc...
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Higher WZW Terms. This is the topic of the next session of the Higher Cartan Geometry Seminar [1]. I'll explain how every higher cocycle on an L-infinity algebra has a "differentially refined" Lie integration to a higher degree analog of the famous gauge coupling term in the Wess-Zumino-Witten sigma model for strings propagating on group manifolds. We'll see how, generically, these higher WZW terms are not defined just on fields which are maps of a worldvolume into a smooth higher group, but rather into a bundle of moduli stacks for differential cohomology over that group. This means that in addition to "embedding fields" there are higher gauge fields on the worldvolumes of the branes described by these higher WZW terms. These include the famous "tensor multiplet" fields on the worldvolume of D-branes and on the M5-brane. 

Letcture notes are at [2]

[1] http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry
[2] http://ncatlab.org/nlab/show/geometry+of+physics+--+WZW+terms
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Corrections to brane charges in M-theory algebra. The extended M-theory supersymmetry algebra is, more or less, known in the literature to be the algebra of supersymmetry Noether currents of the M5-brane sigma-model, which receives the central extension due to the fact that the kappa-symmetry WZW term in the M5 Lagrangian is preserved by supersymmetry only up to a divergence. For the M2-brane this was famously argued in 

José de Azcárraga, Jerome Gauntlett, J.M. Izquierdo, Paul Townsend,
"Topological Extensions of the Supersymmetry Algebra for Extended Objects",
Phys.Rev.Lett. 63 (1989) 2443 

and the extension of this argument to the M5 was indicated in

Dmitri Sorokin, Paul Townsend,
"M-theory superalgebra from the M-5-brane",
Phys.Lett. B412 (1997) 265-273 (arXiv:hep-th/9708003)

Now, these articles consider infinitesimal (super-)symmetries only, and already for this case the argument that it is the de Rham cohomology classes of the brane currents, instead of their differential form representatives that drop out of the Noether procedure, is, I believe this is fair to say, a littel vague.

I did now (or so I think) an analysis of the full M-theory group (in fact it is a super 6-group), i.e. of the global object whose elements are the finite supersymmetries of the full globally defined M5 brane WZW term on curved supermanifolds in the presence of a globally defined M2-brane condensate, equipped with the finite gauge transformations that relate the full transformed WZW term to itself. This reveals a global effect that is not otherwise visible, and my question here is if some incarnation of this effect has surfaced elsewhere, and if so, if anyone could provide me with some pointers, thanks.

Namely I find that the "naive" extension of the superymmetry group on an 11-dimensional spacetime X is not in general just the expected H5(X)⊕H2(X) (5-brane charges and 2-brane charges, including their time components which dualise to the KK-monopole charges and the "M9" brane charges, thus accounting for all the species of M-branes) but that this is just the E2page of a spectral sequence whose relevant non-trivial differential is a d4:H1(X)→H5(X) and d4:H2(X)→H6(X) in direct analogy to the familiar d3in the Atiyah-Hirzebruch spectral sequence for D-brane charges down in 10d .

So intuitively this says that part of the charge of wrapped M5-branes  which naively seems to contribute to the extended M-theory supersymmetry may potentially get cancelled by some kind of 1-brane charge, and similarly that part of the naively present M2-brane charge is actually absorbed by some kind of 6-brane charge.

For the first statement there seems to be an immediate physical interpretation, by the charges of self-dual strings inside the 5-branes which are the boundaries of M2s ending on the M5s. For the second statement I am not sure about the physics interpretation, would be grateful for any suggestions, it looks like it should come from M2s binding with KK-monopoles.. (Though I should emphasize that while the above two differentials are the only two that are potentially relevant, they may happen to not contribute after all.)

A directly analogous differential to the d4 that I find here, but being a d7, has been argued in 

Hisham Sati, Craig Westerland,
"Twisted Morava K-theory and E-theory"
(arXiv:1109.3867)

to encode M-brane charges as d3is well-known to encode D-brane charges. Possibly the d4that I am seeing is an electric-magnetic dual of that d7, but there seem to be some differences. Not sure yet.

My question is if anything related to these d4-corrections have appeared anywhere before in the literature.


For the above text with hyperlinks see here:

http://www.physicsoverflow.org/30795/correction-to-brane-charges-in-m-theory-algebra
The extended M-theory supersymmetry algebra is, more or less, known in the literature to ... have appeared anywhere before in the literature.
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Manifolds and Orbifolds... and  Étale ∞-Groupoids, that's the topic of the next session of the Higher Cartan Geometry seminar [1]. Lecture notes are here:

http://ncatlab.org/nlab/show/geometry+of+physics+--+manifolds+and+orbifolds

We'll first see how to reformulate the definition of manifolds in terms of a modal operator, then see that passing this to smooth groupoids gives  étale groupoids and hence orbifolds, and then further passing all the way to smooth infinity-stacks gives what elsewhere are called higher or derived schemes, in much generality. We'll see how from the neat axiomatization via that model operator follow immediately, by some elementary categorical yoga, that these higher manifolds/étale ∞-groupoids have frame ∞-bundles and that the frame ∞-bundle of a cohesive ∞-group is trivialized by ∞-left translation.

That's the structure that one needs in order to set up higher Cartan geometry proper, which will be the topic of the session after the next one.

[1] http://ncatlab.org/schreiber/show/Higher+Cartan+Geometry 
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The Reader Monad and Random Variables. The function monad [W,-] (aka "reader monad" [1]) has the right to be thought of as producing spaces of random variables on the "probability space of possible worlds" W.

Who agrees with this, in citable print?

I see that +Olivier Verdier does [2]:

"The intuition behind the Reader monad, for a mathematician, is perhaps stochastic variables. A stochastic variable is a function from a probability space to some other space. So we see a stochastic variable as a monadic value."

Also Toronto-MacCarthy10 have this statement [3, slides 23, 24, 35]:

"you could interpret this by regarding random variables as reader monad computations".

Who else?

[1] http://ncatlab.org/nlab/show/function+monad
[2] http://www.olivierverdier.com/posts/2014/12/31/reader-writer-monad-comonad/
[3] http://jeapostrophe.github.io/home/static/toronto-2010ifl-slides.pdf
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Ah -- so necessarily is "in every world p holds the 'same way'" and possibly is "in some world, p holds" and "contextually" or "configurably" or "randomly" is "in every world, p holds, but not necessarily in the same way" or "p obeys a distribution across the worlds". (the latter being much more suggestive!). I see the idea at least, I think.
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Regarding Russell's famous attitude [1] towards Aristotle's logic [2], I have come to wonder if in the course of a justified frustration about an enormous time span of intellectual stagnation, Russell maybe missed an opportunity to recognize a few excellent aspects of Aristotle's logic, which, after dismissing them, took much effort to be rediscovered by Russell himself and then eventually by other people.

Here I am thinking of the fact that Aristotle's logic, while certainly naive and inaccurate from a modern perspective, has the exceptional feature of being a primitive kind of type theory [3].

Where Aristotle says "All A are B" we should recognize what in modern systems would be a function of types A -> B (maybe a monomorphism, if you insist, making A a subtype of B).

Where Aristotle says "Some B1 are B2" this is clearly to be read as an intersection of types, what in modern categorical logic is called a fiber product.

From this perspective, two complaints that are frequently raised against Aristotle's logic seem to be easily transmuted into virtues:

Some of Aristotle's deductions really depend on some silently assumed context. While that means that these were inaccuracies back then, today we easily know how to fix this right away: all types should be regarded as dependent types [4] that exist in some context, to be specified.

Another common complaint is that as Aristotle's types move from the subject of a judgement to the predicate, they seem to turn from types to propositions. For instance on the one hand Aristotle speaks of the collection of all mortal beings, on the other hand he speaks of the proposition "X is mortal". But there is no need to complain about this, in fact this very conflation is a famous accomplishment of modern logic, famous as the Curry-Howard isomorphism or the propositions-as-types paradigm. [5]

Summing up then, we see a logic with a concept of function types and product types formed in context. That's precisely the ingredients of locally Cartesian closed categories of types, which is what modern dependent type theory is about [6]

This is a bit ironic, because it is Russell him very self who, right after rejecting Aristotle, runs into the paradoxes of the young modern logic and is then the one to introduce the modern fix to these: types. See the references [7].

I came to think of this when following Lawvere's suggestion to keep an eye open for hidden insights in Hegel that are invisible to first-order logic but that begin to make a great deal of sense in modern categorical logic and type theory. Since Hegel likes syllogisms, that made me wonder. I have collected a few further details on what I have in mind at [8].


[0] http://philosophy.stackexchange.com/a/23060/5473

[1] http://ncatlab.org/nlab/show/Logic+as+the+Essence+of+Philosophy
[2] http://ncatlab.org/nlab/show/Aristotle's+logic
[3] http://ncatlab.org/nlab/show/type theory
[4] http://ncatlab.org/nlab/show/dependent+type+theory
[5] http://ncatlab.org/nlab/show/propositions+as+types
[6] http://ncatlab.org/nlab/show/relation between category theory and type theory
[7] http://ncatlab.org/nlab/show/type%20theory#References
[8] http://ncatlab.org/nlab/show/Science+of+Logic#FormalizationText
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+Dan Piponi , thanks for saying this, this is much the feeling I have, too.

 The criticisms raised by Russell in [1] seem to be attacking straw men more than the actual substance. But,  conversely the mainstream opinion then that "Aristotle had discovered everything there was to know about logic" [2] was just as fallacious, and I suppose Russell was rebelling really against this intellecutal laziness. But in any case, we as of today should be able to look back at it all and draw some useful conclusions. I am aware of only two articles that go in the direction of suggesting that Aristotle's logic has a useful formalization in categorical logic or type theory

Marie La Palme Reyes, John Macnamara, Gonzalo Reyes ,
"Functoriality and Grammatical Role in Syllogisms"
Notre Dame J. Formal Logic 35 no.1 (1994) pp.41-66.
http://projecteuclid.org/euclid.ndjfl/1040609293

and

Ruggero Pagnan,
"A diagrammatic calculus of syllogisms",
Journal of Logic, Language and Information July 2012, Volume 21, Issue 3, pp 347-364 
http://arxiv.org/abs/1001.1707

Both contain the proposal that Aristotle's "All A are B." is to be interpreted as a function between types. I think that's the right starting point, but then from there on both these articles continue to make it much more complicated than it really is, it seems to me. 

[1] http://ncatlab.org/nlab/show/Logic+as+the+Essence+of+Philosophy
[2] http://plato.stanford.edu/entries/aristotle-logic/
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nLab now running on HoTT grant. As of this weekend, the nLab [1] is hosted on a server at Carnegie-Mellon University that is kindly provided by +Steve Awodey via his MURI grant [2] for Homotopy Type Theory research [3]. 

Thanks to +Michael Shulman for initiating this, to Joseph Ramsey for physically handling the server at CMU and to +Bas Spitters  for catalyzing the process. Thanks a million to +Adeel Khan for administrating the installation and carrying through the migration!

(I had set up the nLab in November 2008 and have been paying for the server ever since, for a while jointly with Andrew Stacey. The new development is a relief.)

Incidentally, the nLab is just passing a nominal entry count of 11,111

[1] http://nlab.preschema.com/nlab/show/HomePage
[2] http://homotopytypetheory.org/2014/04/29/hott-awarded-a-muri/
[3] http://ncatlab.org/nlab/show/homotopy%20type%20theory
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Higher Eilenberg-Moore-toposes of left exact derived comonads. It is a classical fact [1] that for an (accessible) right adjoint comonad on a (sheaf) topos, its Eilenberg-Moore category of coalgebras is itself a (sheaf) topos.

I suppose this remain true for ∞-toposes, for hypercomplete ∞-stack ∞-toposes at least? (But not assuming that the comonad is idempotent.)

[edit: the answer is here: https://plus.google.com/+UrsSchreiber/posts/EeVK6PMoBtF]

[1] http://ncatlab.org/nlab/show/topos+of+algebras+over+a+monad#ToposProperty
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Differential Operators are coKleisli Morphisms of the Jet coMonad. The following statement may be "well known but not well known enough". Do you know a reference which would state it explicitly?

The construction of Jet bundles [1] is a comonad on suitable bundles over a given base X. A differential operator D:Γ(E1)→Γ(E2) is equivalently [2] a morphism of bundles of the form ~D:Jet(E1)→E2 (the associated differential operator is ϕ↦~D∘j∞(ϕ)). Under this identification, the composition D2∘D1of two differential operators is given by the coKleisli composite [3] of ~D1 with ~D2.

In the context of differential geometry, the article

Joseph Krasil'shchik, Alexander Verbovetsky,
"Homological Methods in Equations of Mathematical Physics" 
http://arxiv.org/abs/math/9808130

has essentially all the ingredients for this statement (p. 13,14,17), but does not make it explicit in the above form. In the algebraic context there may be more references that state it this way or almost state it this way (the statement that Jet is a comonad for sure, but how about the differential operators being coKleisli maps?). Whatever references you are aware of, please let me know.

http://mathoverflow.net/q/206405/381


[1] http://ncatlab.org/nlab/show/jet+bundle
[2] http://ncatlab.org/nlab/show/differential+operator
[3] http://ncatlab.org/nlab/show/co-Kleisli+category
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I had emailed Michal Marvan, he had kindly sent me the scan. 
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HoTT in Hamburg. The program for the homotopy type theory meeting in September is now available at https://sites.google.com/site/dmv2015hott/
This webpage contains information about the mini-symposium on Homotopy Type Theory and Univalent Foundations taking place at the convention of DMV 2015 (German Mathematical Society).
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True, that's sad. Maybe the organizers weren't aware of the homotopy between the two subjects?
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German Mathematical Society meeting 2015 takes place in Hamburg this September. I'll be giving two talks:

One in the "Algebra"-section and one in the "Homotopy Type Theory"- mini-symposium:

1) Obstruction Theory for Parameterized Higher WZW-Terms. I present a general characterization of the obstructions for higher WZW-terms (higher gerbes with connection) defined on some higher (or derived) group stack G/H to have a parameterization over higher Cartan geometries locally modeled on G/H. Applied to the canonical Kostant-Souriau line bundle the construction reproduces metaplectic pre-quantization. For the traditional degree-3 WZW term it reproduces the Green-Schwarz anomaly; for the degree-7 WZW term we get a Fivebrane-analog, for the degree-11 term a Ninebrane-analog. Applied to the exceptional cocycles on extended super-Minkowski spacetimes the construction yields a forgetful infinity-functor on globally dened (classical anomaly free) Green-Schwarz super p-brane sigma models propagating on higher super etale stacks, which sends these to G-structures on these super stacks, for G the higher Heisenberg group stack of the higher WZW term. Specically for the super-5-brane sigma-model this yields a forgetful infinity-functor from its classical anomaly free backgrounds to super etale 3-stacks satisfying the equations of motion of 11-dimensional supergravity and satisfying a further topological constraint. Notes are here: http://ncatlab.org/schreiber/show/Obstruction+theory+for+parameterized+higher+WZW+terms


2) Some thoughts on the future of modal homotopy type theory. In 1991 Lawvere suggested a) that the future of category theory revolves around toposes equippped with adjoint system of idempotent (co-)monads [1] and that b) this is formalization of what the ancients had called the "objective logic" [2]. While for 1-toposes this seems inconclusive, one finds [3] that internal to infinity-toposes equipped with such adjoint systems much of higher differential geometry and of modern physics has a succinct and useful synthetic formalization. But here the syntax of this internal language is modal homotopy type theory [4]. In this talk I survey the immensely rich semantics and the potential prospects of  its full syntactic formalization, in the hope to motivate the type theory community to further look into this fascinating but under-explored aspect of their theory.

[1] http://ncatlab.org/nlab/show/Some+Thoughts+on+the+Future+of+Category+Theory
[2] http://ncatlab.org/nlab/show/Tools+for+the+advancement+of+objective+logic
[3] http://ncatlab.org/schreiber/show/differential+cohomology+in+a+cohesive+topos
[4] http://ncatlab.org/schreiber/show/Quantum+gauge+field+theory+in+Cohesive+homotopy+type+theory
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I see what you are getting at. I may very well be naive about how much of the conference cost is siphoned off by para-conference profiteers. And you also have a valid point that not all potential participants would have a local travel/expense budget to cover these costs.
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