I'm in a PhD program and I'm preparing myself to meet a prospective advisor for the first time. I want to know what questions do they usually ask students in their first meeting? What do they expect? I've looked at the following discussions and they were helpful but did not answer my question completely.
From the perspective of the prospective advisor, their goal in the meeting will be to determine whether they want to take you on as a student, so their questions are likely to be based on accomplishing this goal. This is very much like a job interview with a prospective employer, so you should prepare yourself in the same way.
(1) Make sure you have "done your homework" on the research interests of the advisor, and whatever research group they are in. This means that you should have read their faculty webpages, read about the projects they have done, and have a reasonable idea of the kinds of publications that advisor has done. I would expect that you have at least looked at the list of papers published by the advisor, and if you are well-prepared, you might even have skim-read a couple of them. You might be asked questions about why you want to be supervised by that advisor (or work within that group), and you should be able to respond to these with specifics.
(2) Depending on how this university works, you should either have some existing knowledge of projects that they want to put you on, or if you are expected to come up with your own project, you should have some reasonable ideas for this. If you are proposing your own ideas, make sure that they are within the expertise of the prospective supervisor, or else consider a different prospective supervisor. If you have already constructed a research proposal, bring this with you. You may be asked about your ideas for projects, or broad fields of research, and in this case the most important thing to do is to make sure you can explain your ideas in clear and simple terms. When a potential supervisor asks you to describe a project idea, often they are just looking to see if you can communicate your idea in clear non-technical terms to someone who has never heard it before. They want to know that you can communicate about your subject clearly, without falling into a muddle, or giving a stream of jargon.
(3) Your prospective advisor might ask you about your previous experience and courses, to get an idea of your level of existing knowledge. If you have sent them a CV and academic transcript in advance then this will help to narrow down the questions. Some advisors like to ask detailed questions about past courses, grades, etc., and others will just assume that if you got into the PhD program then you have the desired background. This varies a lot, but be prepared to talk about your past education/work, and give some highlights of things you have done well in (without appearing to brag).
(4) You ought to be able to make a plausible case for how you will fit into the advisor's research group, and how you can add value to this group. Expectations will be modest here, since you are a novice, so they are not going to expect you to have any expertise that is lacking in the research group. Still, you should be prepared to explain why you think you would fit well into that research group/project, and show that you have the potential to learn the material rapidly.
(5) Make sure you display an attitude of eagerness and flexibility, and are not too rigid in your desire to work on a particular project. A prospective supervisor will generally look for a student who is able to be slotted into projects where they are needed, and who can adapt to changes in a research project. At the level of a PhD candidature your supervisor will also generally want you to have a broad interest in the field, rather than a narrow interest only in a particular project. It is therefore helpful if you can display an enthusiasm and knowledge for the your field generally. (Some PhD students occasionally ask if it will harm them to show interest in multiple research subjects at once, on the basis that this might dilute their commitment to one project. Although academics often become highly specialised, this is not an expectation that applies to starting PhD students, and at this early stage it is best if the student has a broad interest in the discipline.)
Initial meetings with a prospective supervisor vary wildly, depending on the attitude of that academic. For some academics it is treated as little more than an informal meet-and-greet, while others may ask detailed questions and "grill" the prospective student. So, hope for the best, but prepare for the worst!
The best I can do is to let you know what I ask and want to talk about in these situations. I have worked with 30 Ph.D. advisees in my engineering faculty career to date.
I will not ask technical questions in the same way I would on an oral examination. But, I will certainly bring up technical ideas closely related to my research that I would expect an interested student to know at least a bit about. If the student has something interesting to say on these ideas, then I know that they are seriously interested in my research. I will say that it is better if the student admits that they do not know much about an area rather than "pretend" to be better informed than she/he really is. I'll have to say that I value honesty in these settings above all else.
I will be very interested to understand why the student wants to get a Ph.D., so she/he should be ready to talk about career goals with some specificity. In my view, it is not enough to simply say that they wish to have a career as a faculty member. Why? Where? What do they hope to accomplish?
I'd like to know a bit about their research goals. What types of research are most interesting? What impact do they hope to have with their research and scholarship? What journals do they hope to publish in?
Finally, and probably most importantly, I like to see some evidence of passion about a research problem or subfield or a particular aspect of academic research or the academic career. Students who have a passion to accomplish something and then can set goals that enable them to make it happen are the ones we want to work with most.
I hope this helps!