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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory 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 differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity grothendieck 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 homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory kan lie lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure-theory 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 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 science 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 type type-theory universal variational-calculus

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- Discussion Type
- discussion topicNew Spaces for Mathematics and Physics
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Feb 8th 2020

I have started a category:reference page

such as to be able to point to it for reference, e.g. from Kontsevich 15 etc.

- Discussion Type
- discussion topicMarek Filakovský
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 8th 2020

brief

`category:people`

-entry for hyperlinking references at*computational topology*

- Discussion Type
- discussion topicFrank Verstraete
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 8th 2020

brief

`category:people`

-entry for hyperlinking references at*tensor network*and elsewhere

- Discussion Type
- discussion topiclocale
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by Todd_Trimble
- Last Active Feb 8th 2020

added to locale a section relation to toposes stating localic reflection

- Discussion Type
- discussion topicKolmogorov product
- Category Latest Changes
- Started by PaoloPerrone
- Comments 2
- Last comment by Todd_Trimble
- Last Active Feb 8th 2020

- Discussion Type
- discussion topiccomputational topology
- Category Latest Changes
- Started by Tim_Porter
- Comments 9
- Last comment by Urs
- Last Active Feb 8th 2020

I have started an entry on computational topology partially to record some ideas from some books on that area that I am reading at the moment. There are also new entries on topological data analysis and sources in computational topology.

- Discussion Type
- discussion topicLukáš Vokřínek
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 8th 2020

- Discussion Type
- discussion topicperfect tensor
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 8th 2020

- Discussion Type
- discussion topictree tensor network state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 8th 2020

- Discussion Type
- discussion topictensor network
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Feb 8th 2020

The term “tensor network”, while essentially just a synonym for “string diagram”, has in recent years become widely used and now fully established in quantum physics, especially in its use for discussion of

*holographic entanglement entropy*. It needs a page of its own, if only to point to*string diagram*while also listing the relevant physics references

- Discussion Type
- discussion topicp-adic AdS/CFT correspondence
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Feb 8th 2020

- Discussion Type
- discussion topicsolid state physics
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Feb 8th 2020

added pointer to this discussion of possible realization of the SYK-model in condensed matter physics:

- D. I. Pikulin, M. Franz,
*Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system*, Phys. Rev. X 7, 031006 (2017) (arXiv:1702.04426)

- D. I. Pikulin, M. Franz,

- Discussion Type
- discussion topicBTZ black hole
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Feb 8th 2020

- Discussion Type
- discussion topicAnton Zabrodin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 8th 2020

brief

`category:people`

-entry for hyperlinking references at*p-adic string theory*

- Discussion Type
- discussion topicp-adic string theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Feb 8th 2020

Preprint today by Yau et al., relating $p$-adic strings to the Riemann zeta function:

- An Huang, Bogdan Stoica, Shing-Tung Yau,
*General relativity from $p$-adic strings*(arXiv:1901.02013)

- An Huang, Bogdan Stoica, Shing-Tung Yau,

- Discussion Type
- discussion topicdecidable subset
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Feb 7th 2020

- Discussion Type
- discussion topicBrian Swingle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

brief

`category:people`

-entry for hyperlinking references at*tensor network state*and*holographic entanglement entropy*

- Discussion Type
- discussion topictopological state of matter
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

added these pointers on classification of topological phases of matter via tensor network states:

C. Wille, O. Buerschaper, Jens Eisert,

*Fermionic topological quantum states as tensor networks*, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)Andreas Bauer, Jens Eisert, Carolin Wille,

*Towards a mathematical formalism for classifying phases of matter*(arXiv:1903.05413)

- Discussion Type
- discussion topicKazhdan's property (T)
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

- Discussion Type
- discussion topicMarkov category
- Category Latest Changes
- Started by PaoloPerrone
- Comments 2
- Last comment by nLab edit announcer
- Last Active Feb 7th 2020

- Discussion Type
- discussion topicconcept with an attitude
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Oscar_Cunningham
- Last Active Feb 7th 2020

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.

(…)

- Discussion Type
- discussion topicJens Eisert
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

brief

`category:people`

-entry for hyperlinking references at*tensor network*and at*holographic entanglement entropy*

- Discussion Type
- discussion topicholographic entanglement entropy
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Feb 7th 2020

created a stub for

*holographic entanglement entropy*in reaction to this MO question.

- Discussion Type
- discussion topicRoman Orus
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

brief

`category:people`

-entry for hyperlinking references at*tensor network*

- Discussion Type
- discussion topicstring diagram
- Category Latest Changes
- Started by nLab edit announcer
- Comments 30
- Last comment by nLab edit announcer
- Last Active Feb 7th 2020

- Discussion Type
- discussion topicUli Wagner
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

brief

`category:people`

-entry for hyperlinking references at*computational topology*

- Discussion Type
- discussion topicBruhat-Tits tree
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

a stub for the moment just so as to give a home to

- Bill Casselman,
*The Bruhat-Tits tree of $\mathrm{SL}(2)$*, 2014 (pdf, CasselmanOnBruhatTitsTree2014.pdf:file)

and to cross-link with

*p-adic AdS/CFT correspondence*and*tensor network states*.- Bill Casselman,

- Discussion Type
- discussion topiclambda-ring
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 7
- Last comment by nLab edit announcer
- Last Active Feb 7th 2020

I edited lambda-ring, added a definition from the thesis of John R. Hopkins. Later on I will add the definitions of Hazewinkel, too. This entry has a long (and very instructive) idea-section. Maybe I find time to fill in some more details to these ideas.

- Discussion Type
- discussion topiccosmic inflation
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Feb 7th 2020

stub for

*cosmic inflation*(for the moment just to record some references)

- Discussion Type
- discussion topicJoseph Polchinski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Feb 7th 2020

added pointer to today’s

- Raphael Bousso, Fernando Quevedo, Steven Weinberg,
*Joseph Polchinski: A Biographical Memoir*(arXiv:2002.02371)

- Raphael Bousso, Fernando Quevedo, Steven Weinberg,