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I am going to apply for some postdoc positions which last more than one year. As usual, one of the main required documents is research plan. Having considered some good questions in academia.stackexchange such as Research plan without a specific goal? , Research proposal for postdoc applications and Research Plan that works?, I have another question:

In the case of more than one year postdoc positions, how can I cover several years with one research plan? In other words, I am thinking on some different projects to conduct during these years. Can I mentioned in my research proposal (plan) all of them which are less related to each other? One of them is a kind of my research work in my Ph.D program and the others are further away from my thesis project. In fact, besides working on some aspects of my Ph.D thesis, I would like to work on other topics. As an example, let suppose I worked on pure math and for future I have some plans to work on some applied math. My reason is based on my interests on both of them. In addition, I think by conducting research on projects related to my thesis in first year of my postdoc , I will be able to obtain quick results to provide progress in my research work.

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You can cover several years with one research plan by putting the different projects on a fictive timeline.

You can mention multiple of them but they have to have a logical connection. I don't have experience in mathematics (I did a PhD in Life Sciences), but one important point for postdoctoral application is to show that you can do research in an independent manner i.e. that you understand what topic of research is interesting/relevant, the hypothesis you develop regarding this topic, the approach you choose, and the key experiments which would lead to the results to answer your hypothesis.

An another point is that the research can be done during the timeline of the granted money, i.e. it is realistic and achievable. It is also hard at this stage because you might not know yet but you need to have an educated guess at it. That's why that in terms of number it is also up to you to decide if you should include all of them or not. Regarding possible failure of the plans, try to include the ideas which are innovative and challenging enough but at the same time easy for you (because of your PhD experience) to do in realistic timeframe.

In your case, the hardest part of the grant proposal is to convince the reader that there is a logical approach between these different parts you want to study. If there are no connection at all then it will be difficult to do so and I would advise to not include all of them.

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