Context: I am currently a 4th-year PhD student in Computer Science (Theory), expected to graduate next year (gosh, this went by quickly). Since I end up finding more questions I'd be interested in solving that time or brainpower to actually solve them all, I am maintaining and keeping for myself a list of cute, elegant, or interesting (IMO) research problems I'd like to solve at some point, or see solved. (Preferably, the former.)
I have mentioned a few of these questions to friends or during open problem sessions in workshops, and currently a (subsampled version) of this list is hidden somewhere on my academic website for ease of access.
Question: what are the pros and cons of making this list actually public? I am specifically thinking along the following axes:
Research: while I suppose advertising problems I deem interesting can only be good for the field I am in (i.e., the more solved, the better!), is there any downside?
Short-term interests: to be blunt, I like these problems, and I do believe at least some of them are good ones. I'd be rather sad if some other people methodically solved all of them without me, although it's a bit selfish of me. (Especially if I do spend some time on some of them before my graduation -- I only have that much time left to get new results and consolidate job applications for postdocs...)
Long-term interests: well, sooner or later I'd like to have a position in academia, and who knows even advise students. As far as I can tell, being able to suggest research ideas (from small problems to bigger questions) taylored to a student's interest is a big part of the job: should I try and keep as many as these questions as possible in case I may need them sometime for this purpose?
(I may have forgotten things to consider, or be overthinking that a lot... basically, the point is that my inclination is to put this list online ("of course, why not?"), but would like to be sure there is not actually a good reason not to do so.)
Edit: something I had forgotten to mention.
Some of these problems, I really would like to see them solved, and I fear that I may not have the right set of tools (yet?) or (let's be honest) sufficient insight/intellect to achieve it by myself. Ideally, I'd love to see someone get interested in them, and possibly start a collaboration (best case scenario) leading to a solution. But I'd hate to see these questions get buried and forgotten, fading into oblivion without ever being addressed — just because I kept them to myself.