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I was recently looking at the survey article of Fu on symplectic resolutions which has a number of open questions and conjectures at the end. (I think one of these was existence of a classification of when symplectic singularities admit symplectic resolutions, which is discussed on other MathOverflow questions).

Another perhaps simpler question which was mentioned was whether there is a proof that Coulomb branch varieties are always symplectic singularities. Has any progress been made towards a proof of this or is it of similiar difficulty to the other question I mentioned?

Edit: I'm slightly surprised that no-one has answered this question. It seems like people who work on these types of thing are not very active on Math Overflow for some reason, I'm not sure how that is meant to help people who wish to learn more about the subject.

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    $\begingroup$ Sorry, which survey article by Fu do you mean? The one I found arxiv.org/abs/math/0510346 from 2005 does not seem to mention Coulomb branches (I think they had not been introduced yet by BFN at that time). $\endgroup$
    – Yellow Pig
    Commented Jun 10, 2020 at 6:28
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    $\begingroup$ This new paper arxiv.org/abs/2005.01702 by A. Weekes answers your second question in the case of quiver gauge theories. $\endgroup$
    – Yellow Pig
    Commented Jun 10, 2020 at 9:13
  • $\begingroup$ Perhaps you would have got more answers if you had answered Yellow Pig's question. $\endgroup$
    – abx
    Commented May 1, 2021 at 15:02
  • $\begingroup$ Hi abx, I corresponded privately with Yellow Pig when they contacted me and did answer their question: I did not then feel the need to post the same answer here. $\endgroup$
    – Hollis Williams
    Commented May 1, 2021 at 17:18

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There is a very recent paper by G. Bellamy that shows that every Coulomb branch is a symplectic singularity.

The paper is very nice. You can find it here

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