I’ve collected a few useful details on UC Davis graduate admissions on this page.
1) For most grad programs at Davis you apply to the program as a whole rather than to someone’s research group or lab, and are considered alongside all the other candidates for that year. This is true for Applied Mathematics and Neuroscience, the graduate groups I’m currently part of (see below if you’re applying to another grad group but interested in working with me).
2) There will be a place on the application to list faculty you’re interested in working with, and please do list me if you’re interested. I often (though not always) get a chance to look at applications even if I’m not on the admissions committee, and admissions committees usually try to take faculty preferences into account (though these are one consideration among many other factors).
3) If you are accepted and considering coming and are interested in working with me, do reach out. I usually try to meet with accepted students.
4) If you decide to come to Davis, you typically spend your first year or two both taking classes and looking for a research group/adviser that’s a good fit. The process is a bit more formal in Neuroscience, where students do lab rotations. In Math, students often approach faculty to do reading courses in an area of interest. At the end of this process, students join a research group that feels like a good fit on both sides.
5) Sometimes an adviser is not accepting new students or it’s not a good fit, so it’s wise to apply to programs that include several faculty you could imagine working with.
6) The graduate programs at Davis are organized into graduate groups that include faculty from multiple departments (which makes for a rich culture of interdisciplinary work). I am part of the Applied Mathematics and Neuroscience Graduate Groups. I have in the past worked with students from other graduate groups. If you’re applying to another graduate group that’s close enough to my area, it should be possible for us to work together (though not guaranteed). This would potentially involve me joining that graduate group, if that’s possible, or co-advising you with another mentor.