Applying to math PhD programs this fall and really struggling with my SOP. For math it feels like there's way less to write about compared to social sciences my research experience is basically reading groups and one REU project in combinatorics lol. How specific should I be about research interests? I'm broadly interested in algebra and combinatorics but haven't narrowed it down much. Should I name specific faculty I want to work with or is that too presumptuous? Also how long should the SOP be? I keep going back and forth between too short and too rambly.