This is a question about how to best convey research done to an admissions committee for graduate school.
I have basically two combating philosophies, both may be wrong:
state the "official name" of a paper that is either in preparation, published, or on the arXiv. Follow this with collaborators and perhaps the year you worked on the project.
State the field " Number Theory," state collaborators, and give a brief description of what we accomplished: "We classified classically integral quadratic forms that fail to represent at most two positive integers." Then give where the article was published and its name.
I guess for communication purposes, I like the latter, but I've never seen this done. That being said, I also have some research that is niche enough that the title will not be well-understood by a general audience of mathematicians.
Secondly, I don't like the first since it creates an asymmetry if I want to mention that I am currently doing research on my CV. I guess I can expand on my research experiences in a personal statement, but I figured that a brief description here is helpful.
I guess I want to convey the type of research I've done, since it is a bit diverse (not that much, but pretty broad) so I just wanted to know if there is a good way to proceed.
I think that option (1) is more professional, but also not helpful as it might as well say "I did X number of research projects, and this is their status."