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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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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
   • CommentTimeDec 31st 2017
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexMaybe of interest. A contribution to ICM2018 * [[Yuji Tachikawa]], _On 'categories' of quantum field theories_, [arXiv:1712.09456](https://arxiv.org/abs/1712.09456)

   Maybe of interest. A contribution to ICM2018

   • Yuji Tachikawa, On ’categories’ of quantum field theories, arXiv:1712.09456
2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 2nd 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI see the author has received quite some [recognition](http://www.ipmu.jp/en/node/2328).

   I see the author has received quite some recognition.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 2nd 2018
   • (edited Jan 2nd 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the pointer, I had not seen this article. Have added a pointer as a survey to [[FQFT]]: [here](https://ncatlab.org/nlab/show/FQFT#Tachikawa17). But after first reading I am unsure what to make of this. In the text I see a sketch of the general picture of FQFT and a number of evident but (as far as I am aware) vague relations and widely unproven conjectures. This being invited to ICM suggests that some of these have been made theorems, but which are these? I suspect the author is being honored for contributions to the [[AGT correspondence]] and in the review the distinction between the exciting broad picture of FQFT and the hard results got de-emphasized in the course of trying to make it more expository. (?)

   Thanks for the pointer, I had not seen this article. Have added a pointer as a survey to FQFT: here.

   But after first reading I am unsure what to make of this. In the text I see a sketch of the general picture of FQFT and a number of evident but (as far as I am aware) vague relations and widely unproven conjectures. This being invited to ICM suggests that some of these have been made theorems, but which are these?

   I suspect the author is being honored for contributions to the AGT correspondence and in the review the distinction between the exciting broad picture of FQFT and the hard results got de-emphasized in the course of trying to make it more expository. (?)

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 3rd 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexHe says >we need to discuss the ‘categories’ formed by QFTs and possible operations in those categories. In this note, a rough description of these ‘categories’ will be given, and a few recent mathematical conjectures, some of which are now proven theorems, will be phrased in this language, and then in a footnote >This note is an abridged but updated version of a longer review article intended for mathematicians, which is available on the author’s webpage I can't see it [there](https://member.ipmu.jp/yuji.tachikawa/), even though there's a [page](https://member.ipmu.jp/yuji.tachikawa/not-on-arxiv.html) for papers not on the arXiv.

   He says

   we need to discuss the ‘categories’ formed by QFTs and possible operations in those categories. In this note, a rough description of these ‘categories’ will be given, and a few recent mathematical conjectures, some of which are now proven theorems, will be phrased in this language,

   and then in a footnote

   This note is an abridged but updated version of a longer review article intended for mathematicians, which is available on the author’s webpage

   I can’t see it there, even though there’s a page for papers not on the arXiv.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 3rd 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. Possibly what is meant is the document "On some conjectures extracted from supersymmetric quantum field theories" ([pdf](https://member.ipmu.jp/yuji.tachikawa/transp/conjectures.pdf)) described as > A shorter version of the document above, with less discussions on pseudo-mathematics and more emphasis on better-formulated conjectures. This seems to have much overlap with the second part of the arXiv article.

   Thanks. Possibly what is meant is the document “On some conjectures extracted from supersymmetric quantum field theories” (pdf) described as

   A shorter version of the document above, with less discussions on pseudo-mathematics and more emphasis on better-formulated conjectures.

   This seems to have much overlap with the second part of the arXiv article.