Talking about Your Research vs. Prof at School X's Research

[roboticsapplicant]

In writing my SOP, my first instinct is write as much as I can about the bunch of research projects I've done. Obviously, there isn't enough space to do all of that, so I've focused on the ones that are important and relevant. I have about a short paragraph listing professors and research projects I'd like to work with/on at the school I'm applying to do, and the fact that I believe it would be a good fit cause it matches some of the research I've done previously.

How do you balance talking about yourself, your accomplishments, and your research vs. talking about professors and research being done at the school you're applying to? Is one brief paragraph enough? Should I write essentially a research proposal? Part of me tells me they already know they're cool and have enough brains to look at my listed research and say "hey, this is exactly what I'm doing now", but part of me wonders if all they want to hear about is themselves.

Thoughts?

[anonyouknow]

I spent a short paragraph on each of the professors I mentioned wanting to work with too, tying each of those paragraphs in with my previous experience in the area to save some space and connect it all up. I think a brief paragraph is fine as long as it's clear why you're specifying their names, if it's a good fit with past research it should be clear why you're interested in working with them.

I did throw in an extra mention of the professors' labs and how the recent research from there was of interest to me as well in order to develop a more developed breadth of knowledge in the field, etc etc. More than anything I just used that sentence to point out that I've been keeping up to date with my POI's recent work and would be entering the program with knowledge of what's going on past just my specific interest.