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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundle bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory itex k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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- Discussion Type
- discussion topicasymptotic safety
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active May 8th 2020

- Discussion Type
- discussion topicmodel category
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active May 8th 2020

tried to polish a little and slightly expand model category, starting with the Definition-section and ending with the (new and tiny) Properties section. Added some more subsections and so on.

- Discussion Type
- discussion topicJeff Smith
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 4
- Last comment by Urs
- Last Active May 8th 2020

- Discussion Type
- discussion topicPhilip Hirschhorn
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active May 7th 2020

- Discussion Type
- discussion topicDaniel Kan
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active May 7th 2020

- Discussion Type
- discussion topicrelative category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active May 7th 2020

- Discussion Type
- discussion topicsemimodel category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active May 7th 2020

- Discussion Type
- discussion topicmath blogs
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by Oscar_Cunningham
- Last Active May 7th 2020

- Discussion Type
- discussion topicdilatino
- Category Latest Changes
- Started by Luigi
- Comments 4
- Last comment by Urs
- Last Active May 7th 2020

- Discussion Type
- discussion topicD=5 Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active May 7th 2020

- Discussion Type
- discussion topicsugaring
- Category Latest Changes
- Started by David_Corfield
- Comments 12
- Last comment by David_Corfield
- Last Active May 7th 2020

Started sugaring.

- Discussion Type
- discussion topicThomason model category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 3
- Last comment by Tim_Porter
- Last Active May 7th 2020

- Discussion Type
- discussion topicD=5 Maxwell theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 6th 2020

starting something, for the moment mainly to give a home to

*relation between 5d Maxwell theory and self-dual 3-forms in 6d – section*

- Discussion Type
- discussion topicLaplace operator
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 6th 2020

stated the definition $\Delta f = \star d \star d f$ and spelled out how this gives the usual component formula:

$\begin{aligned} \star d \star d f & = \star d \star (\partial_j f) d x^j \\ & = \star d \left( \tfrac{1}{ \color{green} (D-1)! } \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } \, g^{ i j} (\partial_j f) \, \epsilon_{ i {\color{green} k_2 \cdots k_{D} } } d x^{ \color{green} k_2 } \wedge \cdots \wedge d x^{ \color{green} k_{D} } \right) \\ & = \star \partial_{ \color{magenta} k_1} \left( \tfrac{1}{ \color{green} (D-1)! } \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } \, g^{i j} (\partial_j f) \, \epsilon_{ i {\color{green} k_2 \cdots k_{D} } } d x^{ \color{magenta} k_1 } \wedge d x^{ \color{green} k_2 } \wedge \cdots \wedge d x^{ \color{green} k_{D} } \right) \\ & = \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } \underset{ = \det\big( (g_{i j})^{-1} \big) \delta^{ \color{magenta} k_1 }_i }{ \underbrace{ \tfrac{1}{ { \color{orange} D! } { \color{green} (D-1)! } } \epsilon_{ \color{orange} l_1 l_2 \cdots l_D } g^{ { \color{orange} l_1 } { \color{magenta} k_1 } } g^{ { \color{orange} l_2 } { \color{green} k_2 } } \cdots g^{ { \color{orange} l_D} { \color{green} k_D } } \epsilon_{ i {\color{green} k_2 \cdots k_{D} } } } } \, \partial_{ \color{magenta} k_1 } \left( \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } g^{i j} (\partial_j f) \right) \\ & = \frac{1}{ \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } } \delta^{ \color{magenta} k_1 }_i \partial_{ \color{magenta} k_1 } \left( \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } g^{i j} (\partial_j f) \right) \\ & = \frac{1}{ \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } } \partial_{i} \left( \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } g^{i j} (\partial_j f) \right) \end{aligned}$

- Discussion Type
- discussion topicbrane
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by David_Corfield
- Last Active May 6th 2020

expanded brane

first a little remark on what D-branes are abstractly, in reply to an MO-question, then something on fundamental branes, going along with the discussion on the Café

- Discussion Type
- discussion topicLuigi Alfonsi
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active May 6th 2020

- Discussion Type
- discussion topicdouble field theory
- Category Latest Changes
- Started by Luigi
- Comments 21
- Last comment by Urs
- Last Active May 6th 2020

Hello,

I noticed DFT page has not been updated in a while and I added a couple of sections: some sketchy introductory material (analogy between Kaluza-Klein and DFT) and a little insight about a more rigorous geometrical formulation of DFT.

It is still quite sketchy but I would be happy to refine it.

PS: this is my first edit, I hope I played by the rules. And thank you all for this wiki

Luigi

- Discussion Type
- discussion topicHodge star operator
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active May 6th 2020

mentioned two basic properties at Hodge star operator (namely those needed at holographic principle ;-)

- Discussion Type
- discussion topicanti de Sitter spacetime
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active May 6th 2020

earlier today I had created a stub for anti de Sitter spacetime

- Discussion Type
- discussion topicSchwinger effect
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active May 6th 2020

- Discussion Type
- discussion topicD=5 super Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active May 6th 2020

added pointer to more references, in particular these on the relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the D4-brane double dimensional reduction of the M5-brane:

Nathan Seiberg, Sec. 7 of

*Notes on Theories with 16 Supercharges*, Nucl. Phys. Proc. Suppl. 67:158-171, 1998 (arXiv:hep-th/9705117){#Douglas11} Michael Douglas,

*On D=5 super Yang-Mills theory and (2,0) theory*, JHEP 1102:011, 2011 (arXiv:1012.2880)Neil Lambert, Constantinos Papageorgakis, Maximilian Schmidt-Sommerfeld,

*M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills*, JHEP 1101:083, 2011 (arXiv:1012.2882){#Witten11} Edward Witten, Sections 4 and 5 of

*Fivebranes and Knots*(arXiv:1101.3216)Chris Hull, Neil Lambert,

*Emergent Time and the M5-Brane*, JHEP06(2014)016 (arXiv:1403.4532)Andreas Gustavsson,

*Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower*. JHEP01(2019)222 (arXiv:1812.01897)Neil Lambert, Sec. 3.1 and 3.4.3. of

*Lessons from M2’s and Hopes for M5’s*,*Proceedings of the LMS-EPSRC Durham Symposium:**Higher Structures in M-Theory, August 2018*Fortschritte der Physik, 2019 (arXiv:1903.02825, slides pdf)

- Discussion Type
- discussion topicspectral sequence
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Dmitri Pavlov
- Last Active May 5th 2020

I’ve been working on spectral sequence. But not done yet.

- Discussion Type
- discussion topicsubdivision
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Tim_Porter
- Last Active May 5th 2020

Todd had created subdivision.

I interlinked that with the entry Kan fibrant replacement, where the subdivision $nerve \circ Face$ appears.

- Discussion Type
- discussion topicClifford algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 5th 2020

The entry

*Clifford algebra*used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:Just the bare statements so far.

- Discussion Type
- discussion topicspecial unitary group
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active May 5th 2020

added some very basic facts on $SU(2)$ here to

*special unitary group*. Just so as to be able to link to them.

- Discussion Type
- discussion topictensor product of chain complexes
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Richard Williamson
- Last Active May 4th 2020

following public demand, I added to

*tensor product of chain complexes*a detailed elementary discussion of the tensor product $I_\bullet \otimes I_\bullet$ of the (normalized) chain interval with itself, and how it gives chains on the cellular square: in*Square as tensor product of interval with itself*.

- Discussion Type
- discussion topicHausdorff space
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active May 4th 2020

I added some discussion to Hausdorff space of how the localic and spatial versions compare in classical and constructive mathematics, including in particular the fact that I just learned (in discussion with Martin Escardo and Andrej Bauer) that a discrete locale is Hausdorff iff it has decidable equality.

- Discussion Type
- discussion topicmeson
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active May 4th 2020

- Discussion Type
- discussion topicmonadic adjunction
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by nLab edit announcer
- Last Active May 4th 2020

- Discussion Type
- discussion topicHermite polynomial
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active May 4th 2020