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I am a PhD student third year and I almost finished working on a research with my supervisor. I have few research problems in my mind, I told him about one or two but he did not paid that much attention. I want to try one or two research problem on my own. I am little hesitant to ask him about this. Am I suppose to work with him on each research problem during my PhD? I don't know what will be his reaction. What you people will suggest me to do? I strongly believe that I can do it. There is no funding problem. Second part of the question is how to increase the chances of that the research I will on my own will be accepted in some conference ( definitely I can take some help from my supervisor )

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There are two components to this question. "Is it okay to work on my own 'independent' project in a PhD?"

Yes, definitely. The purpose of a PhD is to train an independent researcher. An advisor who feeds their student the tasks or jobs to do throughout their PhD is probably doing them a disservice, as they would not have the opportunity to learn how to devise and carry out their own independent research projects. Being in the third year, you have probably finished your classes and accrued enough research experience to do so. Of course it is expected that you keep your advisor in the loop if you do decide to work on such a side project.

Now, with regards to "What would my advisor think if I worked on my own 'independent' project?"

That depends entirely on the advisor and your funding situation. If you are full supported by a specific grant, it is probably a bad idea to work on an unrelated topic. Ideally, you should work the problem into something which can be related to the grant. Of course, if you are self-funded or have a no strings attached fellowship, things can be more flexible for you.

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There's nothing to stop you having a Friday afternoon project, as long as it doesn't impinge on your normal work. If you keep it within the area of the advisor's work and you come up with some interesting initial results, you can then present that as a viable research topic to pursue further. Younger researchers often suggest bad ideas (nothing wrong with that), which is probably why your advisor is indifferent to your approaches. If instead you can say "I have thought about X, and have these early results Y and Z. What do you think?", you then have something tangible to expand upon.

Also, remember you are unlikely to fully "go solo" whilst a PhD student. Ultimately, your advisor is there to guide your research and has invested time/money in you so you are attached in some respect. They may be involved to a lesser or greater amount day-to-day, but you can't expect to go into a totally separate area without their backing.

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