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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor 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 homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monads monoid monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 science 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 type type-theory universal variational-calculus

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  1. Creating a page with the basic information on the Math-Phys-Cat group.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020

    Thanks. I have slightly tweaked the first paragraph, and added hyperlinks to technical terms.

    Just a suggestion. If you don’t like it, just roll back.

    What do you mean by the “axiomatization problem of astrophysics”?

    diff, v2, current

  2. That's nice! Thank you very much.

    By the "axiomatization problem of astrophysics" I mean to find a suitable definition of what is a "astrophysical system", allowing the possibility to build general results for them. I was previously interested in try to give a nice definition of "stellar system", independent of gravitational model, and try to prove some obstructions to the existence of a class of them.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020

    I see, interesting. Is there some standard reference for “axiomatization problem in astrophysics”. That might deserve an nLab page of its own…

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020
    • (edited Aug 21st 2020)

    I have enclosed, in the source code, a bunch of further technical terms within double square brackets, so that they come out hyperlinked to the respective nLab entries.

    Also made a table of contents appear.

    diff, v2, current

  3. I think not (at least I dont know one). Since the works of Chandrasekhar, astrophysics and mathematics have not been very close. The only references I can give you are two of my works:

    Yuri Ximenes Martins, Daniel de Souza Plácido Teixeira, Luiz Felipe Andrade Campos, Rodney Josué Biezuner, Constraints Between Equations of State and Mass-Radius Relationships in General Clusters of Stellar Systems, Phys. Rev. D 99, 023007 (2019). (arXiv:1808.09306)

    Yuri Ximenes Martins, Luiz Felipe Andrade Campos, Daniel de Souza Plácido Teixeira, Rodney Josué Biezuner, Existence and Classification of Pseudo-Asymptotic Solutions for Tolman-Oppenheimer-Volkoff Systems, Annals of Physics, v. 409, p. 167929, 2019. (arXiv:1809.02281)

    I have some ideas of how to introduce obstruction theory and elliptic methods in the problem, but now I'm working in different things.
  4. This is very nice. Thank you (really!) for all of this. As I told you, this will be a quantum jump for our group.
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020

    Am happy if I could be of help. Nice to see that you are active on these matters!

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020

    Have added your logo to the top right of the page.

    Check if you like it, otherwise we can revert or change, of course.

    diff, v2, current

  5. Amazing! I was planning to try to do something like this. Let me say that your are very efficient, hehe.
    • CommentRowNumber11.
    • CommentAuthorYuri Ximenes Martins
    • CommentTimeAug 21st 2020
    • (edited Aug 21st 2020)
    It would be a honor to do something with you. Currently I'm working with some different things:

    1) in studying algebra-valued (higher) gauge theories;
    2) in proposing an axiomatization to "strong emerge phenomena" between Lagrangian field theories are get existence results of such phenomena;
    3) in building a general "geometric regularity theory", ensuring the existence of geometric objects as regular as one needs in a manifold whose atlas is regular enough
    4) in extending some results of mine on geometric obstructions on gravity to supergravity;
    5) in studying another proposal for vertical categorification of Lie algebras (the "Lie algebroidal Categories") which by nature are closed related to Lie algebroids. Actually, every Lie algebroid can be regarded as a Lie algebroidal category and, in this case, the "one point limit" for the Lie algebroid coincides with the "one object limit" for the corresponding Lie algebroidal category. Thus, as Lie algebroidal categories, Lie algebroids are genuine horizontal categorifications of "Lie algebra"
    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020

    Thanks. That reminds, me, I had wanted to ask:

    By “algebra-valued (higher) gauge theories” do you mean something along the lines of homotopical algebraic quantum field theory?

  6. No. By "algebra-valued gauge theories" I mean studying functionals (e.g., YM-like functionals) defined in some subset of $\Omega^1(P;A)$, where $A$ is some algebra fulfilling certain polynomials identities, but not necessarily those defining a Lie algebra. The "algebra-valued higher gauge theories" should be the "higher geometry" version of this. In the "flat case" this should correspond to stufying theories defined on A-valued p-forms.
    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020

    Oh, I see. Okay.

  7. Excluding the “projects page” of our group. Unfortunately, it does not more exist.

    diff, v3, current

  8. Small changes.

    diff, v4, current

  9. just adding a category:people tag

    Valeria de Paiva

    diff, v5, current

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