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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 24th 2009
   • PermaLink
   Author: Urs
   Format: Markdownstarted a still highly stubby entry on [[nonabelian Hodge theory]]. So far all I have is some references and the statement of "Corlette's theorem".

   started a still highly stubby entry on nonabelian Hodge theory.

   So far all I have is some references and the statement of "Corlette's theorem".

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 28th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexmade a note at _[[nonabelian Hodge theorem]]_ in a new section _[Relation between local systems and Higgs bundle](http://ncatlab.org/nlab/show/nonabelian+Hodge+theory#LocalSystemsAndHiggsBundles)_, recording a slick formulation of the nonabelian Hodge theorem in terms of [[differential cohesion]] which I learned from [[Alberto García Raboso]].

   made a note at nonabelian Hodge theorem in a new section Relation between local systems and Higgs bundle, recording a slick formulation of the nonabelian Hodge theorem in terms of differential cohesion which I learned from Alberto García Raboso.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 28th 2014
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexDoes he use the language of differential cohesion or is that your rendering of the result? It interests me to see the diffusion of an idea.

   Does he use the language of differential cohesion or is that your rendering of the result? It interests me to see the diffusion of an idea.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJan 28th 2014
   • (edited Jan 28th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexHe does use that cohesive language, yes. The thesis has a dedicated section 4.1 "Classical Hodge theory -- Towards cohesive structures". (The "towards" refers to the fact, that over the algebraic site the shape modality exists only on pro-types.) Of course I enjoy seeing the cohesion, but also apart from that its a rather beautiful thesis. I suppose it should be publically available soon.

   He does use that cohesive language, yes. The thesis has a dedicated section 4.1 “Classical Hodge theory – Towards cohesive structures”. (The “towards” refers to the fact, that over the algebraic site the shape modality exists only on pro-types.)

   Of course I enjoy seeing the cohesion, but also apart from that its a rather beautiful thesis. I suppose it should be publically available soon.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJan 28th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added a pointer to * [[Ron Donagi]], [[Tony Pantev]], _Lectures on the geometric Langlands conjecture and non-abelian Hodge theory_, 2009 ([pdf](http://www.icmat.es/seminarios/langlands/school/handouts/pantev.pdf))

   I have added a pointer to

   • Ron Donagi, Tony Pantev, Lectures on the geometric Langlands conjecture and non-abelian Hodge theory, 2009 (pdf)
6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJan 27th 2015
   • PermaLink
   Author: Urs
   Format: MarkdownItexThat thesis by Alberto Raboso mentioned above is now out as [arXiv:1501.05872](http://arxiv.org/abs/1501.05872)

   That thesis by Alberto Raboso mentioned above is now out as arXiv:1501.05872

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeOct 1st 2023
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAdded redirect [[nonabelian Hodge correspondence]], and some references * wikipedia [nonabelian Hodge correspondence](https://en.wikipedia.org/wiki/Nonabelian_Hodge_correspondence) Gothen's paper starts with a survey on nonabelian Hodge correspondence, * Peter B. Gothen, _Higgs bundles and the real symplectic group_, [arXiv:1102.4175](https://arxiv.org/abs/1102.4175) * C. C. Liu, S. Rayan, Y. Tanaka, _The Kapustin--Witten equations and nonabelian Hodge theory_ Eur. J. Math. __8__ (Suppl 1) 23--41 (2022) [doi](https://doi.org/10.1007/s40879-022-00538-4)

   Added redirect nonabelian Hodge correspondence, and some references

   • wikipedia nonabelian Hodge correspondence

   Gothen’s paper starts with a survey on nonabelian Hodge correspondence,

   • Peter B. Gothen, Higgs bundles and the real symplectic group, arXiv:1102.4175

   • C. C. Liu, S. Rayan, Y. Tanaka, The Kapustin–Witten equations and nonabelian Hodge theory Eur. J. Math. 8 (Suppl 1) 23–41 (2022) doi