Thank you for your interest in Princeton's PhD program. Please note that when applying to our program, it is best to mention at least two faculty with whom you would like to work during your time as a PhD student. While I am not currently looking to accept "primary" advisees, I could be available as a "secondary" advisor, and so you should feel free to mention that in your application. Best wishes with your application process!
Please do also note my policy on speaking with prospective students (copied from below, my notes from 2013 and 2014):
I often receive emails from prospective Ph.D. applicants with requests to talk about my work and what it would be like to do research with me. As of 9-8-13, I decided to refrain from having these personal conversations in advance of reading all applications, because I do not wish to favor students who received advice about how to connect with prospective advisors or who have connections to me through my current colleagues. Before we make final admissions decisions in our department, we fly out our top candidates to visit the campus, and to have one-on-one discussions with their desired mentors and with graduate students and researchers in the department. I view this as the time when the candidates and prospective mentors can have these types of conversations, to figure out whether Princeton (and my research group) would be a good fit.
Outside of the application process, I'm always open to requests for conversations about the topics and methods of the research we are involved with here in my lab. Please do feel free to get in touch with those types of questions.
Thank you for your interest in our research!