How can one best seek out collaborators in obscure topics as a young researcher?

Question

Some context: I will be starting a Ph.D. program in mathematics this fall (a 5 year, U.S. program), and I have a wide array of research interests. In the majority of these areas, I have a (relatively) broad conceptual knowledge, and a few ideas for potential research projects, but I don't think that my command of the material is sufficient to allow meaningful contributions on my part (viz. writing publication-worthy papers) without collaboration.

For example, I have developed a type theory I believe to be compelling for qualities both philosophical and technical. This intellectual endeavor would benefit from the experience and specialized reference of a more knowledgeable collaborator who could elevate my general understanding and vision of how to go about proving the relative consistency of this type theory and enrich the discourse in parts where my experience may be more limited. This brings me to my question: How should I go about seeking (and attracting!) potential collaborators for such a project given my lack of experience in the field?

One other issue that I should mention is that most of these projects are relatively far outside the faculty/student's areas of expertise at my university, so I don't think these projects (like the type theory example given above) would be reasonable for my dissertation, or more generally collaboration with my peers/the faculty at the university I will be attending.

Should I put projects like these on hold until I finish graduate school, make more connections, and have more academic freedom, or is it worth it to try to reach out to academics who might be interested through e-mail/conferences and try to convince them to co-author papers/collaborate with me? I'd appreciate any input on how to best approach this dilemma, but some things I've already thought of are:

1. Type up a short analysis of the literature to ensure potential collaborators that I've done my research, and give an argument of why this research might be significant.

2. Correspond with potential collaborators via e-mail with more pointed questions relating to the potential research question before formally asking if they would like to co-author a paper/collaborate.

Any other input along those lines I think would be helpful, but I think I'd also like to get some context on how my position might fit into the general academic etiquette of the mathematical community, and how someone in my situation might best approach different researchers as a newcomer to the research community.

Thanks in advance for any responses!

Answer 1

As mentioned by aparente001 in the comments, the best way to start collaborations as a beginning PhD student is through your supervisor.

Your supervisor is hopefully a well-established researcher who's made some decent contributions to the field. People working on close areas of research will likely know their name and what kind of things they work on, and consequently the sort of things their students are likely to be doing.

Your supervisor may bring up the idea of collaboration without you asking, or you could approach them with the idea you have and, if it has merit, they might suggest names of people working on similar areas whose work you could read up on and get in touch with.

In this day and age, it's easy to start a conversation through email, and your second point about corresponding with potential collaborators and asking questions about their work is a good approach, but make it clear who you are, what you're working on and why you're interested in their work from the outset.

If you're serious about starting collaborations with people completely outside your network (or your supervisor's network), the best way to do it is face to face, at conferences, meetings or summer schools. The latter are particularly useful for PhD students, as the attendees are also going to be PhD students or post-docs, who will definitely have more time and incentive to start new collaborations than senior academics will.

Lastly, don't worry too much! People are aware that new PhDs are still finding their feet in academia, and as long as you are professional in your enquiries, I don't think you'll go far wrong. It's certainly not bed etiquette to want to work with different people and broaden your research horizons.