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:
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.
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!