Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry 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 lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory object 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 set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 7th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded a couple more references. <a href="https://ncatlab.org/nlab/revision/diff/arithmetic+Chern-Simons+theory/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/arithmetic+Chern-Simons+theory/7">v7</a>, <a href="https://ncatlab.org/nlab/show/arithmetic+Chern-Simons+theory">current</a>

   Added a couple more references.

   diff, v7, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 7th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexOne more. <a href="https://ncatlab.org/nlab/revision/diff/arithmetic+Chern-Simons+theory/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/arithmetic+Chern-Simons+theory/7">v7</a>, <a href="https://ncatlab.org/nlab/show/arithmetic+Chern-Simons+theory">current</a>

   One more.

   diff, v7, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2020
   • (edited Jan 8th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for adding these pointers. Here is a fascinating connection, maybe you could help me explore it: Yau et al make a strong case for p-adic string theory in * [[An Huang]], [[Bogdan Stoica]], [[Shing-Tung Yau]], _General relativity from $p$-adic strings_ ([arXiv:1901.02013](https://arxiv.org/abs/1901.02013)) where Bruhat-Tits trees play the role of "arithmetic" AdS spacetimes. In * Ingmar Akira Saberi, _Knots, Trees, and Fields: Common Ground Between Physics and Mathematics_ ([doi:10.7907/Z9VX0DHZ](https://thesis.library.caltech.edu/9896), [pdf](https://thesis.library.caltech.edu/9896/1/Saberi_Ingmar_2016.pdf)) around Figure 4.3 this is related to knot theory. I feel that this is the way to connect to arithmetic Chern-Simons from weight systems on chord diagrams, and hence from Cohomotopy and _Hypothesis H_. But I didn't yet find the time to explore this connection.

   Thanks for adding these pointers.

   Here is a fascinating connection, maybe you could help me explore it:

   Yau et al make a strong case for p-adic string theory in

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

   where Bruhat-Tits trees play the role of “arithmetic” AdS spacetimes.

   In

   • Ingmar Akira Saberi, Knots, Trees, and Fields: Common Ground Between Physics and Mathematics (doi:10.7907/Z9VX0DHZ, pdf)

   around Figure 4.3 this is related to knot theory.

   I feel that this is the way to connect to arithmetic Chern-Simons from weight systems on chord diagrams, and hence from Cohomotopy and Hypothesis H. But I didn’t yet find the time to explore this connection.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 8th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI'm flattered you think I could help. Certainly a fascinating topic. I like Saberi's expository style. Did you see his account of $p$-adic mathematical physics?: * [[Ingmar Saberi]], _Holography and local fields_, ([arXiv:1801.04942](https://arxiv.org/abs/1801.04942))

   I’m flattered you think I could help. Certainly a fascinating topic.

   I like Saberi’s expository style. Did you see his account of $p$-adic mathematical physics?:

   • Ingmar Saberi, Holography and local fields, (arXiv:1801.04942)
5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 8th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the pointer. So to start we need an entry _[[p-adic AdS/CFT correspondence]]_ and record these references there...

   Thanks for the pointer. So to start we need an entry p-adic AdS/CFT correspondence and record these references there…

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 3rd 2022
   • (edited Jul 3rd 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added publication data for this item: * [[Minhyong Kim]], *Arithmetic Chern-Simons Theory I*, in: *Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants*, Proceedings in Mathematics & Statistics **330**, Spinger (2020) &lbrack;[arXiv:1510.05818](http://arxiv.org/abs/1510.05818), [doi:10.1007/978-3-030-51795-3_8](https://doi.org/10.1007/978-3-030-51795-3_8)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/arithmetic+Chern-Simons+theory/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/arithmetic+Chern-Simons+theory/9">v9</a>, <a href="https://ncatlab.org/nlab/show/arithmetic+Chern-Simons+theory">current</a>

   I have added publication data for this item:

   • Minhyong Kim, Arithmetic Chern-Simons Theory I, in: Galois Covers, Grothendieck-Teichmüller Theory and Dessins d’Enfants, Proceedings in Mathematics & Statistics 330, Spinger (2020) [arXiv:1510.05818, doi:10.1007/978-3-030-51795-3_8]

   diff, v9, current

7. • CommentRowNumber7.
   • CommentAuthornLab edit announcer
   • CommentTimeFeb 29th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexAdding reference * Hee-Joong Chung, Dohyeong Kim, [[Minhyong Kim]], Jeehoon Park, Hwajong Yoo, *Entanglement entropies in the abelian arithmetic Chern-Simons theory* &lbrack;[2312.17138](https://arxiv.org/abs/2312.17138)&rbrack; Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/arithmetic+Chern-Simons+theory/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/arithmetic+Chern-Simons+theory/11">v11</a>, <a href="https://ncatlab.org/nlab/show/arithmetic+Chern-Simons+theory">current</a>

   Adding reference

   • Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Jeehoon Park, Hwajong Yoo, Entanglement entropies in the abelian arithmetic Chern-Simons theory [2312.17138]

   Anonymouse

   diff, v11, current