A specific question on writing research statement
They don't only want to hear what they will be working on, and what topics this is related to.
They would like to see how hiring you would lead to new interactions, that is, discussions, collaborations, joint projects and papers, and so forth, in the department and at the university.
So you should outline your research interests and planned research, discuss how this is connected to topics covered by other researchers in the department/university, and highlight where you see possibilities for collaboration.
So no, just connecting to the field, not the person, is not enough.  You collaborate with people, not with fields, and this is what they would like to see.  (Note that this means that you should ideally have a specific look at the people you might want to work with, and make it concrete where you see room for collaboration (&quot;this opens up the possibility for collaborations with Prof. X, e.g. on the topic of [specific idea 1 and 2}&quot;.), rather than staying very general. Ideally, i should be a statement tailored to those people, not a generic statement.)