Background: Although this site is most-often used for specific one-off questions, many of the highest scored questions (also on MathOverflow), which gather a lot of attention to the site are about informal lists. So, in the theme of, but in contrast to, past questions like:
Question: What are some conjectures of your own?
Specifically, I'm looking for conjectures / problems that
- Have taken up your interest especially (perhaps it was made aware to you, and / or few others),
- Not particularly in public knowledge,
- And that you think are novel (and are comfortable sharing!).
Basically, problems that you find yourself coming back to, that a fellow bored mathematician would find interesting too. All fields welcome.
Note 06/09/23: Let me be clear to appease @user1729 who was worried that people were answering in the form of "I'm great because I came up with this amazing conjecture!", this is not for self-gratification, but to share a problem which is personal to you, for the sake of sharing not because it's yours.
Motivation: If you couldn't already tell, I enjoy recreational mathematics, but all my current problems either bore me or have hit a dead end. I enjoy looking at the big unsolved problems (well-known or not), but sometimes I wish I had a list of very small open-problems which are just as novel, but not as hard or daunting. I'm sure others would appreciate such a list.
As a show of good faith (that I'm genuinely interested in looking into your problems recreationally rather than farming points), this is a Community Wiki question (so accumulated upvotes don't inflate my reputation, if any).
Edit: After discussing the reasons for past-closure on meta here, it's come to my attention that some have interpreted this question to put emphasis on the fact that these conjectures are yours, which is not the point. My word-choice is instead to emphasize the fact that the universe of math is so broad and intricate, that I imagine many people have stumbled upon miniature problems which others have not, and that is what I would like to provide this space for. Nobody "owns" conjecture, but many have discovered conjectures that are not known beyond themselves. This is the place to share them.