The admissions process is a complicated process. You can go back throughout all the years of this forum and see that there are plenty of people with excellent profiles who don't get in anywhere. Similarly, there are people who have fairly apparently substandard profiles who get into some fantastic schools. The only general rules are as follows:
- More is (usually) better. More research, more grad courses, more service activities, etc. That being said, there are plenty of students getting into great schools whose only undergraduate research experience was a summer REU or a couple semesters of unpaid research a few times a week.
- Grades do matter, but they're still a single data point. You can have something below a 3.9 and still be competitive for all but the most prestigious schools (and your shots aren't blown there, either). Below a 3.5, you probably won't be competing for top-tier programs, but you can still get into some good schools.
- The PGRE is mattering less and less as time goes on. Between COVID changing the availability of the GRE and PGRE and research showing that the PGRE is a rather poor indicator of graduate school performance, more schools are placing a lower emphasis (sometimes dropping them altogether) on PGRE scores. Obviously a good score is still important for places that want it, but there are plenty of excellent schools that don't even want to see your scores.
- You do not need published papers to get into grad school. Most undergraduates, particularly those doing theoretical research, don't have enough time or make enough contributions to land on big papers. Those that do are rarely lead authors.
- Your letters of recommendation do matter. Try to do good work and build good relationships with people who can attest to your ability as a researcher.
- Your personal statement/statement of purpose matters. This is the one thing that you can control this late in the admissions process, so take the time to make it good.
If any moderators left on this place see fit to remove this and/or ban truthchannel, so be it.