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I'm a recent math PhD, working in Subject X. I had the good luck to give a counterexample to a conjecture in Subject Y, using ideas from X. I don't know much about Y -- in fact I learned the conjecture in a "Y for dummies"-type paper and immediately saw the example. The people I met in Y seemed to be pretty happy about this.

Now I've been invited to give a talk at a big conference about Y. I would of course be delighted to do so, but by the time the conference happens my paper will be about 18 months post-arxiv. I don't really have plans or competence to do further work in Y, and I'm concerned that my paper will be getting stale by the time the conference rolls around. On the other hand, I could give a basic introduction to X and my example, which I think would be interesting to the audience.

Any suggestions as to how to proceed? Should I accept and give a dated talk?

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Personally, I would find a talk like this very interesting (i.e. an introduction to topic X, which I am not very familiar with, aimed at getting to the mentioned example). –  Tobias Kildetoft Jul 29 at 20:00
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I have been in a talk about the speaker's work in twenty years ago. It didn't seem irrelevant at all, because people still following the ideas discussed in his paper. –  Vahid Shirbisheh Jul 30 at 13:50

5 Answers 5

I'm a physics PhD student, so our culture is a little different, but I've seen people give talks that were primarily about work published multiple years ago. So if math culture is anything like physics culture (and what I've heard suggests that the time scales are even longer for you), I don't think it's a bad idea. Especially, considering the fact that you have been invited to give this talk, it seems they want you there despite knowing that your work will have been out for a long time by the time the conference happens.

If you want to inject something new into it, you could consult with some colleagues in subject Y and ask them what the relevance of your counterexample is. Then you could finish your talk with an overview of what they tell you.

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I'm assuming that either your job or the conference (or a mixture of both) is covering your travel + attendance cost. If that is the case you should give your talk on it.

A couple of good reasons.

1) Your employer likely hires PhDs to publish papers and give talks, and invited talks always looks good when you're looking for a promotion or a new position.

2) Because Subject X provided a counter-example, it is likely much more relevant to Y than was previously though. Likely the researchers in Y don't know much about X, and would like to know more.

3) You say you believe the conference attendees would be interested in your talk. This is the reason people attend conferences, to hear about something they don't understand well but find interesting. Don't worry that the paper is a few years old.

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To add one aspect to the other excellent answers here:

Go and give that talk. Even if you don't really have plans or competence to do further work in Y, as you note, the topic seems to be interesting enough to enough people to explicitly invite you. So you never know, you might meet someone at that conference who you could collaborate with in extending your work!

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Yes, you should accept and give the talk. Here's why:

1) You will be providing a public service. Most of science is currently hyper-specialized and practitioners from different disciplines have trouble communicating their findings to each other because of the differences in jargon and mutually familiar techniques. You have managed to bridge a gap and it is very valuable to make more people in Y aware of your techniques from X. There might even be people from a related Subject Z at the conference, and they might also be looking to learn from you.

2) There may be more low-hanging fruit in Y. You state that you are not inclined to pursue subject Y any further. But perhaps there are other current topics in Y where yet another technique from X might make a contribution. Just listen to some talks on Y and talk to the speakers afterwards. Someone might offer to co-author a paper with you, where they do all the work on Y and you provide the proofs from X.

3) You might initiate more fundamental research on X. Why was the conjecture in Y formulated in the first place? Was your counter-example so hard to construct with the tools previously used in Y? Was the counter-example not a viable practical example in Y? How would other techniques from X map to the domain of Y? Perhaps there are aspects in Y that cannot be readily modelled using X. In that case, you might need to generalize some of X or combine it with tools from subject U.

Conclusion: go forth, inspire and be inspired.

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There is nothing wrong with the paper being old.

As an example, I once did a live experiment during a conference, with the attending people as participants in the experiment. Obviously, I couldn't evaluate and write up the data during the conference, although I had to give a talk with first results 24 hours after the experiment. I was also required to submit a paper with the complete results with the postproceedings, and these postproceedings appeared maybe 4 months after the conference and were sent to everybody who attended it that year.

I had to give the talk on the postproceedings paper the following year, when the conference was held again. Of course, it was attended by the same crowd of known faces (it is a conference for a somewhat small community). These were the same people who had heard the first results the year before, and then received the written paper.

Still, the talk was a success. The audience was very attentive during the talk, and I received both really good questions and great positive feedback afterwards, having professors come up to me, an unknown doctoral student, and express interest and praise for my work. They weren't bored at the "old news".

In fact, I don't think they had read the paper from the postproceedings, and that's fine. With the sheer quantity of research produced these days, nobody can keep up with all publications in their core area, and everybody picks only the stuff which has direct implication for their own work. They are still very interested in related topics when they get the occasion to hear about them, and enjoy good work. They just don't seek this information actively.

So, give the talk. It is a way to promote yourself and your work, and also your area X, which can have interesting synergies with Y. I doubt that anybody will have a negative reaction just because the paper has been sitting around for months.

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