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It seems that for publishing papers, it's better if the topic is a trendy topic. In pure math, it seems that these topics include moduli stacks, geometric Langlands, and derived algebraic geometry. Unfortunately, I don't know any of those things. How can I tell which topics I should pursue?

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    Your question is an interesting and general one, not limited to pure math.
    – EarlGrey
    Commented Mar 7, 2022 at 10:59
  • There are one or two, or three, or a hundred, or a thousand other trendy topics too. Ask your advisor.
    – Lee Mosher
    Commented Mar 8, 2022 at 4:25
  • It is interesting to check other people thoughts. My understanding is that the applications of category theory to machine learning, neural networks and algorithm synthesis (e.g. all the Isabelle/Coq formalization efforts of full space of reinforcement learning algorithms starting from AIXI by Hutter) is stuff that is going to explode with immense applications and business opportunities. You should do this in category theory, because machine learning (automatic theorem proving and theorem discovery) should apply to any branch of math. And who said bad things about category theory!
    – TomR
    Commented Mar 8, 2022 at 7:25
  • You should pursue what interests you. If you don't have any interests, then graduate research is probably not for you. Without passion for the topic you really can't succeed. Your adviser, otherwise, is the person to look to for guidance but really this should be a decision that is based on some interest on your part.
    – J...
    Commented Mar 8, 2022 at 16:51

1 Answer 1

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Just a thought on your premise:

It seems that for publishing papers, it's better if the topic is a trendy topic.

That's a problematic assumption.

  • You only know what's trendy after it has been published, not before. Like the stock market, it is very hard to predict the idea market.
  • More specifically, you don't know if what's trendy now will still be trendy in two to six years, which is when you might be able to publish results.
  • (All equal, it seems more likely that the hype cycle has reached the "trough of disillusionment" by then. If so, it might even be best to stay away from trendy topics.)
  • There is more competition in trendy fields. You don't invest in stocks when they are expensive (in high demand/trendy), you invest when they are cheap (less demand/not trendy). So why would you invest in a topic at its prime? When researchers with more experience are flocking to the top outlets, you're better off looking for a different niche.

Having said that, identifying stale topics is easier than predicting trendy topics. Clearly, these are best avoided. By and large, however, don't worry about trends. Chose a topic that you are somewhat good at and that makes you curious. The former gives you a head start. The latter makes it more likely that you get the project to fruition and publication rather than abandon it. And if you don't succeed in publication, at least the journey was fun.

There's always a trade-off between versatility and specialization, but branching out into a different area at some point after your PhD is a skill that looks good on your CV.

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    Related: stats.stackexchange.com/questions/268293/…
    – Galen
    Commented Mar 7, 2022 at 17:46
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    To add onto this good answer, the most impactful papers are those that start a trend, not those that join an already existing one.
    – Sean
    Commented Mar 7, 2022 at 21:48
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    Aw, but I want to read more papers about science that was developed in Star Trek scripts. Commented Mar 7, 2022 at 22:07
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    I think this might be poor advice. Studying things for the sake of it without regard for topicality can hurt you in the academic job market. Hiring committees want to see evidence that you can move into a new areas, create understanding where there is ambiguity/confusion, and (most importantly) get grants for it. Commented Mar 8, 2022 at 1:37
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    @ComptonScattering I'm a sucker for pointed statements, but I've toned it down a bit (see edits). The main point remains, however: Regard for topicality is nice, but predicting topicality is hard. If you have a good prediction method, I'm looking forward to you posting an answer. Commented Mar 8, 2022 at 8:57

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