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(Disclaimer: I'm rather nervous that this isn't appropriate for MathOverflow, but given the contents of my question I don't really know a better place to ask something like this.)

Recently, I've been reading a lot about topics in quantum field theory (QFT) and topological quantum field theory (TQFT). I've consulted many previous threads asking for book and reference recommendations (e.g: here from 2010), and I've thoroughly enjoyed learning about this area of math. It's beautiful stuff, but I have a couple of questions after learning more and more about this subject (by "subject", I mean TQFT).

Question(s): What exactly "comes after" TQFT mathematically? What has it been applied to in recent (say, 5-10 but this is not strict) years? Is TQFT still actively researched, or is it a "dead" subject and if so, what new things have been built off of it?

I’ve tried scouring the internet in search of an answer to this question, but I haven't seemed to find a satisfactory one yet. Most of the resources (and papers that I've found thus far) on TQFT are at least over a decade old and all seem to contain the same material, so part of me has been wondering if I’ve been working towards a dead end? This area of math is so interesting that I sincerely hope that this isn’t the case, but I wanted to ask on MathOverflow in the hopes that someone could provide "next steps" after learning about TQFT (by "next steps", things like papers/books to read, new genres to take a look at, lectures to watch, or even some historical remarks are what I'm referring to here). If (hypothetically) there are simply no such resources available, is there a reason for this sudden drop in usage of the subject? What would be better (or more productive) routes to take in that case?

Thanks for the help! A thoughtful answer to this question would be greatly appreciated.

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    $\begingroup$ I'm not certain what you mean by "comes after". Are you referring to a specific person's temporal narrative? What generally comes "after" is whatever you take an interest in, i.e. the linear narrative should be your own. $\endgroup$
    – Ryan Budney
    Commented Jun 26, 2023 at 3:17
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    $\begingroup$ Presumably you're familiar with the relationship between string theory and TQFT? $\endgroup$
    – Alec Rhea
    Commented Jun 26, 2023 at 4:01
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    $\begingroup$ The holy grail of TQFT would be a prescription for the duality that interchanges the operator quantum numbers and topological quantum numbers of an arbitrary QFT. More prosaically, there is the sub-problem of finding dualities between classes of perturbative intractable QFTs and (inherently nonperturbative) TQFTs. $\endgroup$
    – Buzz
    Commented Jun 26, 2023 at 4:09
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    $\begingroup$ I think a good resource to learn what is currently going on in the area of TQFT is scgcs.berkeley.edu and in particular the "events" tab. For example you can find a recent summer school listed there categorified.net/TQFT2023 with lecture notes etc. There are more events coming up, so you might want to ask the organisers if you could attend. $\endgroup$
    – Abdelmalek Abdesselam
    Commented Jun 26, 2023 at 9:59
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    $\begingroup$ The question asks about “new genres to take a look at”, one example is nontopological functorial field theory, see people.mpim-bonn.mpg.de/teichner/Math/ewExternalFiles/…, and, more recently, arxiv.org/abs/2011.01208 and arxiv.org/abs/2111.01095. $\endgroup$
    – Dmitri Pavlov
    Commented Jun 26, 2023 at 20:08

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