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I am a PhD student in mathematics. Talking to some colleagues on my department I wrote a paper whose subject lies somewhat beyond the interests of my advisor. I gave a talk on it on a couple of seminars.

Unexpectedly I was invited to give a talk on a conference in another country. I have a feeing that my advisor might be unhappy if I go there, in particular he refused to give me any funds for travel. (It might be he does not have any funds, but I still have a feeling that he does not want me to be involved in activities in other fields.) Nevertheless I am interested to present my results to a broader audience and one of the colleagues on the department I talked to agrees to help me with the travel funds.

Would it be ok if I will go to the conference? Is it ethical with respect to my supervisor?

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    If your advisor is not OK with you broadening your horizons and your research directions, then something is not alright. – PsySp May 17 '17 at 13:25
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    We need a "You need to talk to your advisor" autoresponder bot for questions like these. – eykanal May 17 '17 at 13:34
  • A friend of mine was in a similar situation. Then the logic was that the first impression matters, and sometimes it makes sense to take more time to develop professionally and make a stronger "debut". Not sure whether that applies in your case. – 12345 May 17 '17 at 18:11
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    Your adviser's refusal of funding for your travel might have nothing to do with how he feels about your going to the conference. His research funding might come from a grant for research on a particular topic, and he might not be allowed to use that money for purposes unrelated to the topic. – Andreas Blass May 17 '17 at 20:15
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As @eykanal stated, the answer is simply to talk to your supervisor.

To specifically answer your questions:

1- Yes, it is more than OK to go to the conference. Being invited to an international conference is a great achievement that you should be proud of.

2- I don't see how it could be unethical to your supervisor.

I'm not sure from your question if your advisor has already refused the funds. I would suggest to not overthink this. Budget are generally tight. If your supervisor is a normal human being (most are), he's probably proud of your achievement. If for some reasons he doesn't approve, but does not clearly forbid you to go...well that's a strange situation but you can't guess his mind, can't you? If your relation is good, discussing is the only way to know.

Just remember that the goal of the PhD is to create an independent researcher out of you. Not a duplicate of your supervisor.

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    Just remember that the goal of the PhD is to create an independent researcher out of you. Not a duplicate of your supervisor. If only all supervisors were thinking along these lines! – PsySp May 17 '17 at 13:45
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I am not in mathematics, so I'm not sure how much my response is discipline-specific.

One of the roles of an advisor is that of a mentor. If you are presenting a paper at a conference, this is part of professional development and normally it should be supported. However, if the paper is outside of your advisor's field, I do not see why he or she would provide you with funding (if available) for travel, since his or her funding would normally be tied to the work that he or she is doing. Also, if the paper and conference are that different from your advisor's field, he or she may not appear interested or supportive because they do not have enough expertise in the topic to be involved.

In some cases, advisors may be arrogant and feel that their area is important than others. Some also become paternalistic and express disappointment if you are not making decisions that THEY think are best. That does not make your decision to attend the conference unethical. However, you also do not mention "how far" outside the field this paper and conference are from that of your advisor. If it seems that you are going in a different direction altogether in your studies or engaged in activities that seem distracting from your program of study, he or she may be concerned. However, this is not necessarily your case.

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    "However, if the paper is outside of your advisor's field, I do not see why he or she would provide you with funding" - I tend to think something is wrong there already. For instance, I am rather unfamiliar with the concept of "outside of [the] advisor's field". The advisors I know are generally supportive whenever someone opens a door for possible interdisciplinary collaboration; it's one of the best things that can happen. (Of course, a specific grant may require a particular topic.) – O. R. Mapper May 18 '17 at 6:51
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    Well, if I have funding for a conference or for my student to attend a conference, it is usually connected with a grant or contract that would be related to my field. I cannot spend money from a grant on topic A to cover student travel for some other unrelated topic. If the advisor has general funds to cover the student, that is different. I think funding would more appropriately come from the department, not the advisor. – Nicole Ruggiano May 18 '17 at 16:33
  • I can still be supportive of my student and help him or her with the project (reviewing the paper or poster, etc.) without providing travel support. – Nicole Ruggiano May 18 '17 at 16:35
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    Even funding basically "related to a field" can well be available for certain kinds of interdisciplinary research. And aside from that, there are also field-agnostic funding sources such as support programmes for female researchers etc. Anyway, my comment was just meant to address the issue when the advisor does not just lack the funding, but is actively unwilling to support the student, which transpired from both the OP's question ("feeling that he does not want me to be involved in activities in other fields") and from your answer ("I do not see why he or she would"). – O. R. Mapper May 18 '17 at 18:25

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