AnxiousAwaiter

I should have known based on your username, lol. How did the interview/conversation go? Did they give you a sense as to what the process/timing is like?

That's great! What's your field?

TBH, I think the interviews are generally set up for them to ask YOU questions –– not for you to grill them about the program, support, placement records, etc. That type of grilling would be more appropriate once you are accepted and are trying to decide where to go. You would do well to ask general questions about advising, composition of committees, etc., but do NOT ask questions that you can look up on the website. (e.g., "For PhD students entering with an MA in the field, is there an accelerated track for completion of the program? Is this advisable?")

You might also want to look at CUNY Graduate Center's program: https://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Centers-and-Institutes/Latin-Greek-Institute/Programs/Upper-level-Programs-in-Latin-and-Greek