Is Mulmuley's geometric complexity theory program still active?
I tried to look it up online, and I haven't seen anything from the last couple of years.

  • 2
    $\begingroup$ There are some papers, from last year for example arxiv.org/pdf/2211.07055.pdf In general looking for recent papers by Panova and Ikenmeyer, tends to give a good overview of directions. $\endgroup$
    – Ilk
    Mar 2 at 1:23
  • $\begingroup$ Indeed, there are also very recent results: arxiv.org/abs/2401.07631 $\endgroup$
    – domotorp
    Mar 2 at 4:50
  • 2
    $\begingroup$ arXiv:2401.07631 is actually a part of the paper linked by @ilk (I'm a coauthor of these papers, reviewers didn't like the scope of the original paper and suggested to split it). I also would say that while it is about geometric complexity theory widely understood (study of orbit closures of polynomials), it does not have much in common with GCT as it is laid out in Mulmuley's GCT papers. Section 5 of arXiv:2211.07055 is closer. $\endgroup$ Mar 3 at 7:42
  • 4
    $\begingroup$ It is my understanding of the current status of GCT is that the optimistic picture of Mulmuley's GCT papers is more of less understood to not hold, but the geometric and representation-theoretic methods can still be useful, and the general idea that hard polynomials with a lot of symmetries may help in breaking natural proof barriers is still alive. The work now is about trying to understand more about orbit closures, symmetries, multiplicities, and find settings where we can apply this knowledge to get new results, probably not yet at the level close to the P-vs-NP question. $\endgroup$ Mar 3 at 7:58
  • 2
    $\begingroup$ I may write a more detailed answer later, but I'm not sure when I will have time. $\endgroup$ Mar 3 at 8:00


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