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In my field, computational condensed-matter physics, the last author name in a paper is regarded as having a supervisory role. I know this is common to many fields but not all (notably, math).

I am a postdoc associated to a professor's group. By "associated" I mean that I have my own project and funding, on which I am officially and practically the PI. However, I am also carrying out supervisory work of a student in the professor's group, paid from a project on which the professor is the PI. Incidentally, I designed and wrote a large portion (circa 50%) of the proposal for that project, but I have no official attachment to it. Since the project kicked off, I have been redesigning the scope and methods of the project as we progressed through it, and the student is working basically on testing my ideas under my guidance. The professor knows about the main features of what we do but is not familiar with any of the details nor is proposing/contributing significantly to either science or supervision.

Everybody is more or less happy with the arrangement, since the professor sees progress, with minimal cost of his time and effort, on this research area of interest in which he can contribute little due to his lack of background on computational physics. I get some extra manpower to extend my ability to test some of my ideas, and the student gets supervised by someone who can provide expert guidance on the topic of this PhD thesis. The professor is easy going and everybody is in good terms with each other.

However, I am starting to apply for senior positions. In one of my applications, I was rejected mainly on the basis of being too junior, and a piece of critical feedback was on my lack of "last author papers". It had been agreed with the professor that I would be last author in some of the student's first authored papers (actually, he suggested that). However, in a recent manuscript draft where the student put my name last the professor corrected the author list and put his name last instead. This could be because he forgot about the agreement or (I suspect this one) he realized the paper was much more significant than originally expected and wanted to get some "extra" credit for it. This credit is needed for him to increase his chances at future funding in this research direction. However, I feel that this undermines my contribution and does not accurately reflect the role that each author had on the study, since I designed the project, proposed the ideas, did the actual supervision, and even contributed to getting the funding (and thus, the convention in my field dictates that my name should go last). Further to this, I desperately need to get this credit to just stay "afloat" in academia (whereas the professor "only" needs it to increase his funding pool).

I think it is only fair to work out a list of authors that more accurately and fairly reflects my contribution to our upcoming papers. However, I want to avoid falling off with this professor or introducing undue strain into our working relationship. How should I approach a request for my name to appear as last author in subsequent papers?

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Just knock on their door and ask.

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Discussing authorships is a pretty common thing to do and you got a very good reason why having this last authorship would benefit you and I just assume it wouldn't really hurt the professor if he's already established in that field. I would just be very open about the whole situation and explain the problem and ask if that's fine with him.

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