<p>Aggregating comments by  Thomas Klimpel, Sasho Nikolov and  Mohammad Al-Turkistany into a community answer:</p>

<p>The correction (and hence the quasi-polynomial result) was immediately supported by Harald Andrés Helfgott. His expository paper (<a href="https://arxiv.org/abs/1701.04372" rel="noreferrer">https://arxiv.org/abs/1701.04372</a>) and its translation (<a href="https://arxiv.org/abs/1710.04574" rel="noreferrer">https://arxiv.org/abs/1710.04574</a>) are all the support that is needed for the quasi-polynomial results. Helfgott’s exposition appeared as <a href="https://smf.emath.fr/publications/expose-bourbaki-1125-isomorphismes-de-graphes-en-temps-quasi-polynomial-dapres-babai" rel="noreferrer">Exposé 1125</a> in Astérisque 407 (2019), Séminaire Bourbaki 2016/2017, pp. 135–182.</p>

<p>There are no current known issues with Babai’s proof, and it has gone through extensive peer review. That said, even published peer-reviewed papers have later been withdrawn as incorrect. </p>

<p>The support by Harald Andrés Helfgott along with the lack of other issues should be sufficient for us to accept that graph isomorphism is indeed solvable in quasi-polynomial time. </p>

CC BY-SA 3.0
2018-03-14T14:22:30.253Z
In case it's unclear, the thing which is "to appear" in the Bourbaki seminar is Helfgott's exposition, not Babai's paper.
Sasho Nikolov
CC BY-SA 3.0
2018-03-14T14:44:46.747Z
Note I deliberately made this answer a community wiki, not only to not take credit, but anyone including you can easily edit to make any improvements/clarifications.
Meir Maor
CC BY-SA 4.0
2018-03-14T10:01:21.890Z
2019-06-24T16:10:18.913Z
2019-06-24T16:10:18.913Z
Meir Maor
<p>It's been over a year since his January 2017 retraction and correction. 
Is there news?<br>
If not is this normal for validation to take this long? I would expect it would get plenty of attention. 
Has anyone of note spoken up to support/doubt the quasi-polynomial result? </p>

CC BY-SA 3.0
2018-03-11T07:06:19.147Z
The correction (and hence the quasi-polynomial result) was immediately supported by Harald Andrés Helfgott. His expository paper (https://arxiv.org/abs/1701.04372) and its translation (https://arxiv.org/abs/1710.04574) are all the support that is needed for the quasi-polynomial results (as long as no further holes or mistakes are found). There is no news to wait for.
Thomas Klimpel
CC BY-SA 3.0
2018-03-11T07:18:22.743Z
have these been published somewhere?(not arxiv)
Meir Maor
CC BY-SA 3.0
2018-03-11T07:43:41.637Z
It says "To appear in Astérisque. Fascicule no 1125 of the Bourbaki seminar (69th year, 2016-2017)" on arXiv. It has not appeared yet, (http://smf4.emath.fr/Publications/Asterisque/2017/) lists "Séminaire Bourbaki, volume 2015/2016 ", and (http://smf4.emath.fr/Publications/Asterisque/) does not yet list anything from 2018.
Thomas Klimpel
CC BY-SA 3.0
2018-03-11T21:01:40.537Z
It's absolutely normal for a math paper to take more than a year, even more than two years to publish.
Sasho Nikolov
CC BY-SA 3.0
2018-03-13T12:39:59.727Z
On the other hand, Publication of a paper does not mean that the results are correct. There are many cases of results withdrawn after getting published in journals. For instance, https://www.sciencedirect.com/science/article/pii/0020019080900125?via%3Dihub
Mohammad Al-Turkistany
<cc.complexity-theory><graph-isomorphism><proofs>
What's the status of Babai's Graph isomorphism result?
Meir Maor
# What's the status of Babai's Graph isomorphism result?

(Asked by: username_0 on 2018-03-11)

It's been over a year since his January 2017 retraction and correction.
Is there news?  
If not is this normal for validation to take this long? I would expect it would get plenty of attention.
Has anyone of note spoken up to support/doubt the quasi-polynomial result?

**Tags:** cc.complexity-theory, graph-isomorphism, proofs
> **Comments:**
> **username_1**: The correction (and hence the quasi-polynomial result) was immediately supported by Harald Andrés Helfgott. His expository paper (https://arxiv.org/abs/1701.04372) and its translation (https://arxiv.org/abs/1710.04574) are all the support that is needed for the quasi-polynomial results (as long as no further holes or mistakes are found). There is no news to wait for.  
> **username_0**: have these been published somewhere?(not arxiv)  
> **username_1**: It says "To appear in Astérisque. Fascicule no 1125 of the Bourbaki seminar (69th year, 2016-2017)" on arXiv. It has not appeared yet, (http://smf4.emath.fr/Publications/Asterisque/2017/) lists "Séminaire Bourbaki, volume 2015/2016 ", and (http://smf4.emath.fr/Publications/Asterisque/) does not yet list anything from 2018.  
> **username_2**: It's absolutely normal for a math paper to take more than a year, even more than two years to publish.  
> **username_3**: On the other hand, Publication of a paper does not mean that the results are correct. There are many cases of results withdrawn after getting published in journals. For instance, https://www.sciencedirect.com/science/article/pii/0020019080900125?via%3Dihub  

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## 1 answers

### Answer by username_0 on 2018-03-14. Score: 27 | Accepted answer

Aggregating comments by Thomas Klimpel, Sasho Nikolov and Mohammad Al-Turkistany into a community answer:

The correction (and hence the quasi-polynomial result) was immediately supported by Harald Andrés Helfgott. His expository paper (<https://arxiv.org/abs/1701.04372>) and its translation (<https://arxiv.org/abs/1710.04574>) are all the support that is needed for the quasi-polynomial results. Helfgott’s exposition appeared as [Exposé 1125](https://smf.emath.fr/publications/expose-bourbaki-1125-isomorphismes-de-graphes-en-temps-quasi-polynomial-dapres-babai) in Astérisque 407 (2019), Séminaire Bourbaki 2016/2017, pp. 135–182.

There are no current known issues with Babai’s proof, and it has gone through extensive peer review. That said, even published peer-reviewed papers have later been withdrawn as incorrect.

The support by Harald Andrés Helfgott along with the lack of other issues should be sufficient for us to accept that graph isomorphism is indeed solvable in quasi-polynomial time.

> **Comments:**
> **username_2**: In case it's unclear, the thing which is "to appear" in the Bourbaki seminar is Helfgott's exposition, not Babai's paper.  
> **username_0**: Note I deliberately made this answer a community wiki, not only to not take credit, but anyone including you can easily edit to make any improvements/clarifications.  

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