I am naming three professors from specific Ph.D. programs with whom I have identified similarities in our research interests in my SOP. In the last sentence, I want to mention that I am also interested in working with other professors whose research aligns with my own. I want to include this line in case my selected three professors reject me; then, there will be hope that someone else with similar research interests (whom I might have missed while searching the university website) will show interest in my application. However, I understand that the admissions committee or the professors might perceive this as negative. Is writing a sentence at the end of the paragraph expressing that I am open to working with other faculty members with similar research interests a good or bad idea?
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1Are you naming those professors because the institution has instructed you to (e.g.: "name 3 professors you're interested in working with in your application")? Or just on your own accord? – Bryan Krause Dec 07 '23 at 16:58
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Some universities explicitly wanted the names, but most of them didn't. But from whoever I spoke to (and some YouTube videos) they all suggested to name 2-3 professors. – Nahid Hossain Shihab Dec 07 '23 at 17:37
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Some related questions that might be useful: https://academia.stackexchange.com/questions/15016/can-i-mention-professors-names-in-the-statement-of-purpose https://academia.stackexchange.com/questions/116530/can-i-mention-multiple-faculty-members-in-my-sop https://academia.stackexchange.com/questions/120184/mention-a-specific-potential-adviser-and-project-in-the-phd-statement-of-purpose – Bryan Krause Dec 07 '23 at 17:49
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Unlike some other places, in the US it is seldom necessary to specify professors. It is useful, however, to be flexible. You may need to specify some subfield of the overall field, but little else. If you have some ideas for research that is a plus provided you don't insist on this-but-nothing-else.
Focus the SoP on your goals, it is fine to name some professors as possible advisors, but seldom necessary. You generally have a while before you need to choose a supervisor and have a chance to meet them and become more familiar with their work.

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Thank you, but I am not clear yet. Is writing a sentence at the end of the paragraph expressing that I am open to working with other faculty members (I mean, the faculty members I did not mention earlier) with similar research interests a good or bad idea? – Nahid Hossain Shihab Dec 07 '23 at 16:45
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Although I suspect that you're not in mathematics... in which a student's saying they were "willing" to work with ... would sound very arrogant... I think you should not say so. I'd presume that in every milieu most students would be happy to have an advisor/mentor/funding ... so it might be a little silly to say that you would "accept" such things. You're at the low end of the status hierarchy, etc... :) – paul garrett Dec 07 '23 at 22:06